AIRPLANE  CHARACTERISTICS 


By  the  same  author 

The  Principles  of  the  Transformer 
Direct  and  Alternating  Current  Manual 

Experiments  with  Alternating  Currents  (being  Part 
II  of  Volume  II  of  A  Laboratory  Manual  of 
Physics,  edited  by  E.  L.  Nichols) 

Alternating  Currents :  an  Analytical  and  Graphical 
Treatment  for  Students  and  Engineers  (jointly 
with  A.  C.  Crehore) 

Also,  editions  in  French  and  German 


L* 


AIRPLANE 
CHARACTERISTICS 


A  SYSTEMATIC  INTRODUCTION  FOR 
FLYER  AND  STUDENT  AND  FOR  ALL 
WHO  ARE  INTERESTED  IN  AVIATION 


BY 

FREDERICK  BEDELL,  PH.D. 

\  v 

Professor  in  Physics,  Cornell  University 

Member  Aeronautical  Society  of  America,  Vice-President  Amer- 
ican Institute  of  Electrical  Engineers,  Fellow  and  Past  General 
Secretary  American  Association  for  the  Advancement  of  Science, 
Member  the  American  Physical  Society  and  Managing  Editor 
of  The  Physical  Review. 


FIRST  EDITION 
PRICE  $1.60  NET 

See  Note  in  Regard  to  Publication  on  Following  Page 


TAYLOR  AND  COMPANY 

ITHACA,  NEW  YORK 
1918 


NOTE  IN  REGARD  TO  PUBLICATION 

In  view  of  the  importance  at  the  present  moment  of  any  contribution 
to  aviation,  this  first  edition  containing  only  part  of  the  material  con- 
templated is  issued  now.  The  remaining  part,  referred  to  in  the  Preface 
and  Contents,  is  in  preparation  and  this,  it  is  expected,  will  be  ready 
for  publication  in  1919. 

TAYLOR  AND  COMPANY,  Ithaca,  N.  Y.,  will  send  copies  of  this  book, 
postpaid,  upon  receipt  of  $i  .75  per  copy.  Copies  may  also  be  obtained 
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and  from  leading  dealers  generally. 


COPYRIGHT  1918 

BY 
FREDERICK  BEDELL 


PRESS  OF  W.  F.  HUMPHREY,  • 


TO 

FOUR  NEPHEWS  WHO  ARE  IN  THE  AIR  SERVICE  OF  THE  UNITED 
STATES  AND  HER  ALLIES,  AND  TO  THE  MEMORY  OF 
ONE   NEPHEW   WHO   HAS   DIED   IN  THAT 
SERVICE,  THIS  BOOK  IS  DEDI- 
CATED   BY    THE 
AUTHOR 


382818 


PREFACE 

Any  contribution  to  aviation,  however  small,  needs  today 
no  justification.  The  airplane  is  an  accomplished  fact  and 
concerning  it  there  is  no  longer  any  room  for  apology  or 
speculation.  So  far  has  the  art  of  flying  progressed  that  the 
principles  of  flight  can  in  the  main  be  set  forth  as  definite  and 
without  surmise,  and  a  collection  of  the  essential  elements 
can  now  be  made  that  will  apply  to  all  airplanes,  irrespective 
of  type  or  structure.  Not  that  there  is  nothing  further  to  be 
learned  or  discovered  in  aviation — for,  far  from  it,  there  is 
ample  opportunity  for  discovery  and  invention  in  this  direc- 
tion— but  a  codification  of  the  well-known  ground  work  can 
now  be  made  that  may  be  an  aid  to  those  who  are  advancing 
the  art,  as  well  as  to  those  who  are  learning  it. 

The  introductory  discussion  in  this  volume  is  a  contribu- 
tion to  such  a  codification,  which,  it  is  hoped,  will  prove 
useful  not  only  to  the  flyer  and  designer,  for  whom  the  book 
is  primarily  intended,  but  to  students  and  engineers  and  to 
others  who  have  only  a  general  interest  in  aviation.  Indeed, 
so  important  is  the  place  now  taken  by  the  airplane  that 
there  are  many  who  desire  a  knowledge  of  the  principles  of 
its  operation. 

It  is  the  author's  purpose  to  present  the  principles  of  air- 
plane sustentation  and  stability  and  the  characteristics  of  an 
airplane  in  flight  in  a  way  that  is  direct  and  simple  and  at  the 
same  time  reasonably  precise,  laying  particular  stress  on  that 
which  is  vital.  Except  in  minor  ways,  no  claim  is  made  for 
originality  other  than  in  presentation;  in  fact,  the  aim  has 
been  to  include  only  those  things  that  are  essential  and  are 
accordingly  well  known  to  those  versed  in  the  subject.  To 
those  not  thus  well  versed,  the  characteristics  of  an  airplane 


PREFACE 

are,  however,  not  so  well  known  as  they  should  be ;  discussion 
of  the  subject  is  apt  to  be  either  superficial  and  inadequate  or 
involved  and  complicated.  The  author  has  endeavored  to 
give  a  treatment  that  is  adequate  but  simple,  and  without  the 
use  of  higher  mathematics. 

Logical  sequence,  rather  than  historical  development  has 
been  kept  in  mind  and  no  attempt  has  been  made  to  ascribe 
particular  features  to  their  inventor  or  author.  Military 
uses  of  the  airplane,  as  well  as  its  history,  are  left  to  others 
who  may  more  appropriately  discuss  such  phases  of  the 
subject.  The  author  has  confined  his  attention  to  the 
principles  of  airplane  flight  and  has  given  no  discussion  of 
materials  of  construction — very  important,  of  course,  in  air- 
plane building — nor  of  the  gas  engine,  on  which  there  are 
many  specialized  treatises. 

The  author  had  occasion,  as  a  member  of  a  commission  for 
planning  the  courses  in  our  SCHOOLS  OF  MILITARY  AERONAU- 
TICS, to  study  carefully  the  needs  of  such  courses.  He 
has  had  occasion,  also,  to  conduct  several  classes  in  aero- 
dynamics and  the  principles  of  flight,  made  up  not  only  of 
those  with  a  direct  practical  interest  in  flight,  as  future  pilots 
and  designers,  but  likewise  of  others  with  an  indirect  interest 
— students  in  civil  and  mechanical  engineering  and  physics — 
who  have  been  interested  in  the  airplane  as  in  any  of  the 
mechanisms  of  our  present  day  civilization.  He  has  noted 
particularly  those  parts  of  the  subject  that  have  proved  vital 
and  of  interest  to  all, — no  matter  from  what  angle  the  subject 
is  approached. 

It  is  planned  that  the  book — with  the  added  chapters  now 
in  preparation — shall  be  self-contained  and  complete  in  its 
own  field,  i.  e.,  as  an  introduction;  final  practical  instruction 
for  flyer  or  designer  must  needs  be  obtained  at  the  flying 


PREFA  CE 

field  or  in  the  designing  room.  The  author  has  had  flying 
experience  only  as  passenger  and  would  make  no  attempt  at 
specific  flying  instruction. 

In  view  of  the  present  emergency,  it  is  thought  best  to 
issue  the  material  contained  in  this  first  edition  without  delay, 
and  to  reserve  for  subsequent  publication  the  material  now 
in  preparation  (referred  to  in  the  Table  of  Contents)  that  is 
needed  to  complete  the  work.  The  author  will  be  glad  to 
have  his  attention  called  to  any  error  or  obscurity  in  this 
presentation  and  will  particularly  appreciate  constructive 
suggestions  from  those  practically  engaged  in  airplane 
operation  or  development. 


ITHACA,  N.  Y., 
July  30,  1918. 


CHAPTER  I. 
CHAPTER  II. 
CHAPTER  III. 
CHAPTER  IV. 
CHAPTER  V. 
APPENDIX  I. 
APPENDIX  II. 
APPENDIX  III. 
APPENDIX  IV. 


CONTENTS 

Sustentation 

Relations  in  Flight 

Resistance 

Lateral  Stability 

Directional  Stability 

Glossary    - 

Thrust  Characteristics    - 

Power  Characteristics     - 

Control  and  Other  Diagrams 


PAGE 
1 

28 

41 

55 

67 

77 

91 

103 

115 


IN   PREPARATION 

The  following  chapters  are  in  preparation:  Thrust;  Power;  Climb- 
ing; Gliding;  Altitude;  Single  and  Multiple  Planes;  Stability  in 
General;  Longitudinal  Stability. 


AIRPLANE 
CHARACTERISTICS 


CHAPTER  I 

SUSTENTATION 

The  first  essential  for  flight  is  a  sustaining  force  or  sus- 
tentation.  This  is  obtained  in  balloons  and  in  airships 
by  the  buoyancy  of  a  light  gas  which  makes  the  craft  as 
a  whole  lighter  than  air  and  capable  of  flotation.  In  an 
airplane,  or  in  any  aircraft  heavier  than  air,  this  sustentation 
must  be  obtained  by  the  reaction  of  the  air  upon  planes  or 
surfaces  which  are  moving  with  relation  to  the  air  and  which 
force  or  deflect  the  air  downward.  The  airplane  is  the  only 
craft  of  this  kind  that  has  been  practically  developed  and 
it  alone  will  be  discussed  in  this  volume.  Other  types  of 
flying  machines  have,  however,  been  contemplated,  among 
which  may  be  mentioned  the  ornithopter,  with  wings  that 
flap  like  those  of  a  bird  and  sustain  the  machine  by  forcing 
the  air  downward  and  at  the  same  time  backward;  and  the 
helicopter,  equipped  with  propellers  which  revolve  on  a 
vertical  shaft  and  lift  the  machine  by  forcing  the  air  directly 
downward. 

A  second  essential  for  flight  is  stability,  discussed  in  later 
chapters. 

The  sustentation  of  an  airplane  is  due  to  the  fact  that 
the  air  it  encounters  is  deflected  downward  by  the  wings; 
although  this  downward  deflection  is  but  little,  it  is  sufficient 
to  sustain  the  machine,  for  new  air  is  being  continually 
encountered  and  deflected.  An  understanding  of  sustenta- 

1 


2  AIRPLANE   CHARACTERISTICS 

tion  will  best  be  gained  by  a  consideration  of  the  pressure 
exerted  by  the  air  upon  flat  and  curved  surfaces  moving 
rapidly  with  relation  to  it. 

FLAT  PLANE  PERPENDICULAR  TO  AIR  STREAM 

We  will  first  consider  the  pressure  on  a  flat  plane  perpendi- 
cular to  an  air-stream. 

Pressure  varies  as  square  of  velocity. 

If  a  thin  plate  or  plane,  say  a  book  cover  or  the  cover  of  a 
cigar  box,  is  held  out  from  a  moving  automobile  —  well 
away  from  the  body  and  windshield  —  so  that  the  air- 


PRESSURIT    P 

AIR  STREAM 


DIRECTION  OP  MOTION 

Fig.  i.     Pressure  on  flat  surface. 

stream  strikes  the  plane  perpendicularly  to  its  surface,  as  in 
Fig.  i ,  a  pressure  is  felt  that  is  small  at  low  speeds  but  which 
increases  very  rapidly  as  the  speed  increases.  In  fact, 
if  accurate  measurements  were  made,  it  would  be  found  that 
when  the  speed  is  doubled  the  pressure  becomes  four  times 
as  great,  in  other  words  that  the  pressure  varies  as  the  square 
of  the  speed. 

Furthermore,  this  same  relation  would  be  found  to  be 
true  if  the  plane  were  held  still  in  a  wind  or  in  the  air  from 
a  blower,  and  so  it  is  seen  that  the  pressure  depends  not 
upon  the  absolute  velocity  of  the  plane  or  of  the  air  but 
upon  their  relative  velocity,  as  the  air-stream  strikes  the 


SUSTENTATION  3 

plane.  This  is  on  account  of  the  great  mobility  of  the 
air  particles,  the  effect  being  the  same  whether  the  air  is 
stationary  or  moving.  The  law  of  the  "square-of-the- 
velocity,"  although  not  a  general  law  that  holds  for  all  sub- 
stances and  for  all  velocities,  may  be  taken  as  practically 
true  in  air  throughout  the  range  of  airplane  velocities. 

Pressure  varies  with  plane  area. 

By  using  planes  of  different  areas,  it  would  be  found, 
likewise,  that  the  total  pressure  on  the  plane  increases 
with  the  plane  area  and  (practically)  in  direct  proportion 
to  the  area;  for  example,  an  increase  of  ten  per  cent,  in 
area  is  accompanied  by  an  increase  of  ten  per  cent,  in  total 
pressure  on  the  plane.  This  relation,  however,  must  be 
considered  as  only  approximate,  particularly  when  the  planes 
compared  differ  greatly  in  shape  or  area. 

General  law. 

The  total  pressure  P,  upon  a  surface  5,  normal  to  an 
air-stream  with  velocity  V,  may  accordingly  be  expressed 
by  the  following  law: — 

P  =  KSV*. 

Here  K  is  a  number  or  coefficient,  the  value  of  which  depends 
upon  the  units  used*.  When  the  area  5  is  given  in  square 
feet,  the  velocity  V  in  miles  per  hour  and  the  total  pressure  P 
in  pounds,  a  practical  value  for  the  coefficient  K,  that  has 
been  determined  experimentally,  is  0.003  *or  air  at  normal 
density;  that  is, 

P  =  0.003  SV2- 
The  pressure  per  square  foot  of  surface  is  thus  seen  to  be 


*Thus,  when  P  is  expressed  in  ounces  per  square  foot,  the  numerical 
value  of  P,  and  so  of  K,  is  16  times  as  great  as  when  P  is  expressed  in 
pounds  per  square  foot. 


4  AIRPLANE   CHARACTERISTICS 

1.2  pounds  at  a  velocity  of  20  miles  per  hour,  4.8  pounds  at 
a  velocity  of  40  MPH.,  19.2  at  80  MPH.,  etc. 

Metric  units. —  When  V  is  velocity  in  meters  per  second, 

5  the  area  in  square  meters  and  P  the  weight  in  kilograms, 
the  value  of  K  is  0.07  5 .    To  get  K  in  English  units  of  pounds, 
square  feet  and  miles  per  hour,  multiply  K  for  metric  units 
by  0.0408. 

Variations  in  K. 

The  value  of  K  is  not  strictly  a  constant.  It  varies 
directly  with  the  density  of  the  air,  decreasing,  therefore, 
with  altitude,  as  discussed  later,  and  changing  somewhat 
from  day  to  day.  It  varies,  also,  with  the  size  and  shape  of 
the  surface.  The  values  given  above  (K  =  0.003  in  English 

6 


Fig.  2.     Square  with  aspect  ratio  i;  and  rectangle 
with  aspect  ratio  6. 

units,  K  =  0.075  in  metric  units)  are  for  a  square  surface, 
0.15  x  0.15  meters,  in  air  of  normal  density.  For  squares  of 
different  sizes,  experiments  of  Eiffel  give  values  for  K  as 
follows : — 

Length  of  side  .I5m.  -375m.     .500111.     .707111.     i.oom. 

Value  of  K  .066  .0716       .0746       .0772       .0789 

For  rectangles  of  equal  area  (0.225  m.2)  and  with  different 
aspect  ratios  (the  aspect  ratio  is  the  length  divided  by  width, 
see  Fig.  2)  Eiffel  gives: — 

Aspect  Ratio         I  3  6  10  20        30        50 

Value  of  K  .066  .0705  .0725  .0755  .0885  .092  .097 
KR-J-KS  i.  1.07  1. 10  1.145  I-34  MO  M7 

The  last  line,  KR-4-Ks,  is  the  value  of  K  for  a  rectangle 


SUSTENTATION  5 

divided  by  the  value  of  K  for  a  square.  The  percentage 
increase  in  K  with  change  of  aspect  ratio,  shown  in  the  last 
line,  will  hold  approximately  for  rectangles  of  other  areas, 
for  the  effect  of  aspect  ratio  is  almost  independent  of  size  of 
surface. 

Somewhat  different  values  hold  for  circular  discs  and  other 
shapes.  Considerable  experimental  data  must  be  gathered 
before  the  precise  value  of  K  can  be  determined  for  a  surface 
of  any  size  and  shape.  Meanwhile  the  value  0.003  (English 
system)  or  0.075  (metric  system)  will  prove  practically  useful, 


Fig.  3.     Turbulent  region  and  rarefaction  back  of  plane. 

it  being  borne  in  mind  that  this  value  is  only  an  approxima- 
tion and  that  a  closer  value  should  be  sought  whenever  it 
may  be  deemed  desirable. 

Eddies  back  of  plane. 

When  a  plane  encounters  an  air-stream,  there  is  a  compres- 
sion of  the  air  on  the  front  face  of  the  plane.  Immediately 
back  of  the  plane  there  is  a  rarifaction,  so  that  back  of  the 
plane  air  currents  are  set  up  that  swing  around  toward  its 
rear  surface.  These  air  currents  may  be  felt,  by  one  riding 
in  an  open  trolley  car  or  in  an  automobile  behind  a  wind 
shield,  as  a  wind  on  the  back  of  the  neck. 

These  air  currents  are,  in  a  crude  way,  visualized  in  Fig.  3. 


6  AIRPLANE   CHARACTERISTICS 

Back  of  the  plane  and  near  the  edge  is  a  turbulent  region  with 
complex  eddy  currents  of  air.  These  no  doubt  have  a 
material  effect  upon  the  value  of  K,  so  that  it  is  not  surprising 
that  K  has  different  values  for  surfaces  of  different  shapes  and 
sizes,  for  in  these  the  length  of  edge  and  the  eddy-current 
effect  is  not  proportional  to  the  area. 

Methods  of  experimenting. 

Experiments  on  the  air  resistance  of  different  surfaces  or 
bodies  may  be  made  in  various  ways.  The  necessary  velocity 
of  the  body  relative  to  the  air  may  be  obtained  by  dropping 
it  from  a  suitable  tower  or  other  height  (employed  by  Eiffel), 
by  carrying  it  on  a  fast  moving  vehicle,  by  carrying  it  at  the 
end  of  a  long  rotating  arm  (employed  by  Langley),  by 
exposing  it  to  a  natural  wind,  and  finally  by  carrying  it 
through  the  air  in  airplane  flight. 

The  most  convenient  and  approved  method  now  in  use  is 
to  expose  the  body  to  an  artificial  wind  in  a  wind  tunnel,  first 
used  by  Eiffel*  and  now  used  in  all  aerodynamic  laboratories. 
Air  is  forced  through  such  a  tunnel  by  means  of  a  powerful 
fan;  the  body  to  be  studied  is  held  stationary,  being  attached 
to  suitable  devices  for  measuring  the  pressure  and,  in  case  of 
oblique  surfaces,  for  "weighing"  the  vertical  as  well  as  the 
horizontal  component  of  the  pressure. 

In  such  a  tunnel  can  be  tested  not  only  surfaces  or  bodies 
of  various  kinds,  including  wing  sections,  but  even  complete 
airplanes  in  model  size ;  and  it  is  important  to  note  that  the 
performance  of  wings  and  airplanes  in  flight  is  found  to  agree 
remarkably  well  with  wind-tunnel  tests. 


*Eiffel's  experiments  are  beautifully  described  in  his  book  "The 
Resistance  of  the  Air  and  Aviation,"  translated  into  English  by  J.  C. 
Hunsaker. 


SUSTENTATION  7 

FLAT  PLANE  OBLIQUE  TO  AIR  STREAM 

Let  us  next  consider  the  action  of  a  flat  plane  at  an  oblique 
angle  with  the  air-stream ;  such  a  consideration  will  show  at 
once  the  source  of  the  sustaining  force  in  an  airplane. 

Lift  of  an  oblique  plane. 

If  a  plane  be  held  so  as  to  form  an  angle  i  (called  the  angle 
of  incidence  or  the  angle  of  attack)  with  the  air-stream  or 


Angle  fcf  Incidence 


Fig.  4.     Vertical  and  horizontal  components 
of  pressure  on  oblique  plane. 

"relative  wind,"  as  in  Fig.  4,  it  will  be  seen  that  the  total 

pressure  P  of  the  air  against  the  plane  has  two  components:* 

A  vertical  component  or  lift,  commonly  designated 

by  the  letter  L,  tending  to  force  the  plane  upward  at 

right  angles  to  the  air-stream. 

A    horizontal    component    or    dynamic    resistance 

(called,    in   an   airplane,  wing-resistance,)  commonly 

designated  by  the  letter  D,  tending  to  force  the  plane 

backward  in  the  direction  of  the  air-stream. 

These  components  may  be  observed  by  blowing  upon  a  card 

held  in  the  hand  oblique  to  the  air-stream,  or  by  moving  the 


"These  two  components  are  horizontal  and  vertical  only  in  normal 
horizontal  flight.     More  accurately  defined,  lift  is  the  component  of 


8  AIRPLANE   CHARACTERISTICS 

hand — slightly  inclined — rapidly  through  water;  in  the 
latter  case  the  upward  lift  may  be  distinctly  felt. 

It  is  the  lift  that  holds  an  airplane  up  in  flight,  i.  e.y  that 
gives  sustentation ;  for  an  understanding  of  the  airplane, 
therefore,  a  knowledge  of  what  determines  the  lift  is  essential. 
Clearly  for  horizontal  flight  the  lift  must  be  just  equal  to  the 
weight  of  the  machine,  otherwise  the  machine  will  either 
ascend  or  descend, — discussed  later  under  climbing  and 
gliding.  The  problem  of  horizontal  flight  is,  therefore,  the 
problem  of  securing  a  lift  equal  to  the  weight.  As  discussed 
later,  this  lift  is  better  obtained  from  a  "cambered"  wing 
(i.  e.t  a  wing  that  is  slightly  curved  from  front  to  back)  than 
from  a  flat  plane. 

LIFT  LIFT  LIFT  LIFT 

' '  A ' i 

a  bed 

Fig.  4a.     Lift  is  inclined  when  machine  is  inclined. 

In  order  to  get  the  lift,  the  plane  or  wing  must  move 
rapidly  through  the  air.  But  in  order  to  move  the  plane  or 
wing  through  the  air  it  is  necessary  to  overcome  the  wing- 
resistance  and  this  is  done  by  the  thrust  from  the  propeller. 
To  drive  the  propeller,  so  as  to  obtain  this  thrust,  it  is  neces- 

total  pressure  that  is  perpendicular  to  the  air-stream  and  that  lies  in  the 
plane  of  symmetry  of  the  machine;  this  plane  is  vertical  as  long  as  the 
machine  does  not  roll.  Lift  is  accordingly  vertical  in  normal  flight,  but 
becomes  inclined  when  the  machine  is  inclined,  as  shown  in  Fig.  4a. 
Wing-resistance  is,  in  all  cases,  the  component  of  total  pressure  that  is 
in  the  direction  of  the  air-stream. 

It  is  recommended  by  the  U.  S.  Advisory  Committee  on  Aeronautics 
that  the  word  "drift,"  sometimes  used  as  a  designation  for  wing- 
resistance,  be  abandoned;  see  "drift"  in  Glossary,  Appendix  I.  But 
the  initial  letter  D,  in  such  common  use,  may  well  be  retained  as  a 
symbol  for  dynamic  or  wing  resistance;  likewise,  KD,  formerly  called  the 
coefficient  of  drift,  may  be  retained  as  the  coefficient  of  dynamic  or  wing- 
resistance. 


SUSTRNTATION 


9 


sary  to  have  power.  Obviously  it  is  desirable  to  have  the 
wing-resistance  small,  necessitating  small  thrust  and  small 
power,  and  to  have  the  lift  large  so  that  the  machine  can 
sustain  not  only  itself  but  some  load  in  addition.  But  it  is 
impossible  to  have  the  lift  without  the  wing-resistance,  and 
the  wing-resistance  has  aptly  been  described  as  the  price 
paid  for  the  lift. 

Variation  of  lift  and  wing-resistance  with  incidence. 

Highly  important  is  it  to  know  how  the  values  of  lift  and 
wing-resistance  vary  as  the  angle  of  incidence  is  changed. 


Fig.  5.     Flow  of  air  past  oblique  plane,  showing  turbulent  region 

back  of  entering  edge  and  the  downward  deflection 

of  air  after  leaving  the  plane. 

This  information  cannot  well  be  derived  theoretically  on 
account  of  the  complexity  of  the  problem, — due  in  part  to  the 
eddy  currents  in  the  turbulent  region  back  of  the  entering 
edge,  as  indicated  in  Fig.  5.  The  information,  however,  has 
been  found  experimentally. 

The  total  pressure  P,  the  lift  L  and  the  wing-resistance  D 
all  vary  directly  as  the  area  5,  of  the  plane  or  wing,  and  as  the 
square  of  the  velocity  V;  that  is, 

Total  pressure  =  P  =  KPSV2; 

Vertical  component  or  lift  =  L  =  K^SV2; 

Horizontal  component  or  wing-resistance  =  D  =  K^SV*. 


10 


AIRPLANE    CHARACTERISTICS 


We  are  particularly  interested  in  the  two  components  L 
and  D ;  also  in  the  two  coefficients,  K^  called  the  coefficient 
of  lift  and  K&  called  the  coefficient  of  wing-resistance. 

These  coefficients  have  different  values  for  each  angle  of 
incidence.  Their  values,  furthermore,  will  depend  upon  the 
units  used. 

The  values  of  these  coefficients  that  will  give  lift  and  wing- 
resistance  in  pounds,  for  different  angles  of  incidence,  when  5 


o° 


20° 


s°         to0         AS" 

ANGLE  OF  INCIDENCE 

Fig.  6.     Coefficient  of  lift  J£L  and  coefficient  of  wing-resistance  KO 

for  flat  rectangle  at  different  angles  of  incidence;  aspect 

ratio,  6,  i.  e.,  length  -r-  width  =  6,  as  in  Fig.  2. 

is  in  square  feet  and  V  is  in  miles  per  hour,  are  shown  by  the 
curves  in  Fig.  6.  These  are  plotted  from  data  by  Eiffel*  for 
a  flat  rectangle  with  an  aspect  ratio  6. 

For  small  values  of  incidence,  it  will  be  seen  that  the 
coefficient  of  lift  increases  nearly  uniformly,  in  proportion  to 


""'Resistance  of  the  Air,"  p.  122;  size  of  rectangle  90  x  15  cm. 


SUSTENTATION 


11 


the  angle  of  incidence ;  if  the  angle  is  doubled,  the  coefficient 
of  lift  is  approximately  doubled.  After  reaching  a  maximum 
value  (in  this  case  about  0.002)  the  coefficient  decreases 
somewhat  irregularly*,  becoming  zero  at  90°  incidence. 

This  maximum  value  is  only  two-thirds  as  great  as  the 
maximum  value  obtained  by  a  cambered  wing ;  see  Fig.  1 1 . 

The  coefficient  of  wing-resistance  also  increases  more  or  less 
uniformly  with  incidence  and  reaches  a  value  of  about  0.003 
at  90° ;  but  in  no  case  is  KQ  zero,  even  at  zero  incidence. 

e  r     • 


Is 


i: 


-|.40 


30 


20 


10 


5°  10-  IS*  goo 

ANGLE  OF   INCIDENCE 

Fig.  7.     Curves  showing  L/D  ratio  and  D/L  ratio  for  flat 
rectangle;  aspect  ratio,  6. 

Lifting  efficiency  or  L  /D  ratio. 

The  ratio  of  lift  to  wing-resistance,  is  frequently  referred  to 
as  the  lift-over-drift  ratio  or  the  L  /D  ratio,  or  as  the  lifting 
efficiency  of  a  plane  or  wing,  and  this  ratio  is  of  much 
significance.  As  it  is  desirable  to  have  L  large  and  D  small, 


*After  20°,  KL  increases  slightly,  having  by  Eiffel's  data  the  same 
value  at  30°  as  at  15°.  The  incidence  at  which  the  maximum  occurs, 
and  its  value  are  different  for  different  aspect  ratios;  but  the  curves  are 
all  of  the  type  here  shown. 


12  AIRPLANE    CHARACTERISTICS 

it  is  obviously  desirable  to  have  the  L/D  ratio  as  large  as 
possible.  It  is  seen  that  the  L/D  ratio  is  equal  to  KL  -r-  K-Q, 
values  for  which  are  obtained  from  the  curves  in  Fig.  6. 

The  values  of  the  L  /D  ratio  for  a  flat  rectangle  with  aspect 
ratio  6,  thus  obtained  from  Fig.  6  for  different  angles  of 
incidence,  are  shown  in  Fig.  7 .  The  maximum  value  for  L  /D 
is  here  seen  to  be  a  little  over  6  at  an  incidence  of  6°, — a  rather 
poor  lifting  efficiency  compared  with  an  L  /D  ratio  16  or  more 
for  a  cambered  plane. 

In  Fig.  7,  the  values  are  also  shown  for  D  /L  (see  dotted 
curve);  but,  as  these  values  approach  infinity  when  L 
approaches  zero,  they  are  not  so  convenient  to  use.  It  is 
more  usual,  therefore,  to  make  use  of  the  L  /D  ratio. 

In  the  case  of  a  theoretical  plane  with  a  perfectly  smooth 
surface,  the  pressure  P  would  be  perpendicular  to  the  surface, 
so  that  D  /L  would  be  the  tangent  and  L  /D  the  cotangent  of 
the  angle  of  incidence;  and,  at  zero  incidence,  the  resistance 
of  the  plane  would  be  zero. 

But  in  a  practical  case,  the  plate  or  wing  that  is  used  must 
possess  an  edge  of  definite  thickness,  and  this  with  some  skin 
friction  (undoubtedly  small)  gives  a  certain  resistance,  even 
to  a  horizontal  plate.  The  resultant  pressure  P,  shown  by  the 
solid  line  in  Fig.  4,  is,  therefore,  not  perpendicular  to  the 
surface  but  is  a  little  back  of  the  perpendicular, — which  is 
shown  by  the  dotted  line.  Its  direction  and  magnitude  can 
be  determined  by  laying  off  the  two  components  L  and  D, 
the  resultant  pressure  being  P  =  V  L2  +  D2. 

Center  of  pressure. 

When  the  plane  is  perpendicular  to  the  air-stream,  i.  e., 
when  the  angle  of  incidence  is  90°,  the  center  of  air  pressure 
on  the  plane  is  at  the  center  of  the  plane.  When  the  plane  is 


SUSTENTATION 


13 


oblique,  the  center  of  pressure  is  found  to  be  in  advance  of  the 
center  of  the  plane,  moving  more  and  more  forward  toward 
the  entering  edge  as  the  incidence  decreases.  The  position 
of  the  center  of  pressure  for  different  angles  of  incidence  is 
shown  by  the  curve  in  Fig.  8.  The  position  is  somewhat 
different  for  different  aspect  ratios,  but  in  all  cases  with  a  flat 
plane  the  center  of  pressure  moves  forward  from  the  center 


UJ  .10 


ENTERING  EDGE 


TRAILING  EDGE 


15° 


30°  45°  60° 

ANGLE  OF  INCIDENCE 


75° 


90° 


Fig.  8.     Position  of  center  of  pressure  on  a  flat  plane,  with  aspect 
ratio  6,  for  different  angles  of  incidence. 

of  the  plane  as  the  incidence  decreases,  thus  becoming  nearer 
to  the  front  edge  of  the  plane — which  is  called  the  entering  edge 
or  leading  edge — and  further  from  the  rear  or  trailing  edge. 

CAMBERED  WING 
Decreased  turbulance  when  cambered  wing  is  used. 

A  flat  plane  encountering  an  air-stream  disrupts  the  air, 
the  entering  edge,  and  to  a  lesser  extent  the  trailing  edge, 


14  AIRPLANE   CHARACTERISTICS 

tending  to  produce  air  eddies.  The  turbulence  produced  by 
such  a  plane  has  been  shown  in  Fig.  5,  which  as  already 
explained  indicates  the  phenomenon  but  should  not  be  under- 
stood to  be  an  accurate  representation  of  it.  It  would  seem 
that  this  turbulence  would  increase  the  wing-resistance  and 
that  it  might  decrease  the  lift;  or,  put  another  way,  it  would 
seem  that,  if  the  turbulence  could  be  eliminated  or  reduced 
by  any  means — for  example  by  giving  the  wing  more  or  less 
of  a  stream-line  form, — an  increase  in  lift  and  decrease  in 
wing-resistance  might  be  obtained.  This  indeed  is  the  case, 
such  a  result  being  obtained  by  arching  the  wing  from  front 
to  back.  A  wing  thus  arched  is  called  a  cambered  wing  and 
on  account  of  its  better  performance  is  always  used  in  air- 
plane construction. 

The  flow  of  air  past  a  cambered  wing  is  shown  in  Fig.  9, 
which  again  is  merely  illustrative  and  is  not  exact  in  detail. 
The  disturbance  of  the  air  by  the  wing  is  minimized  by  having 
the  surfaces  of  the  wing,  throughout,  more  or  less  parallel  to 
the  stream-line  flow;  the  wing  then  enters  the  air  and  leaves 
the  deflected  air  without  disturbance,  and  eddies  are  elimin- 
ated so  far  as  they  can  be. 

Creation  of  lift. 

It  is  to  be  borne  in  mind  that  it  is  the  downward  deflection 
of  the  air  that  creates  the  lift,  it  being  the  purpose  of  the 
designer  to  increase  this  lift  and  at  the  same  time  to  decrease 
the  wing-resistance.  Lift  is  obtained  to  a  certain  extent  by 
the  positive  pressure  on  the  lower  surface  of  the  wing  (indi- 
cated by  p  in  Fig.  9)  but  to  a  much  greater  extent  by  the 
negative  pressure  on  the  upper  surface,  indicated  by  n; 
indeed,  as  much  as  three-fourths  of  the  total  lift  may  be  due  to 
this  negative  pressure.  It  will  be  seen  that,  in  a  cambered 
wing  as  shown  in  Fig.  9,  the  upward  trend  of  the  upper 


SUSTENTATION 


15 


surface  of  the  entering  edge  swings  the  air-stream  upward 
over  the  wing  before  its  final  deflection  downward;  this 
decreases  the  pressure  on  the  upper  surface  and  so  contributes 
materially  to  the  lift. 

The  distribution  of  pressure  on  single  and  multiple  planes 
is  shown  in  a  later  chapter.  See  Appendix  IV. 

It  is  the  curvature  of  the  upper  surface  of  a  wing  that  is 
most  important, — particularly  its  dip  toward  the  entering 
edge,  often  referred  to  as  the  dipping  front  edge.  The  curva- 
ture of  the  lower  surface  is  far  less  important;  with  a  well 


Fig.  9.     Flow  of  air  past  a  cambered  wing;  side  view. 

formed  upper  surface,  a  good  wing  can  be  constructed  with  a 
perfectly  flat  lower  surface. 

An  upward  turn  in  the  lower  surface  toward  the  entering 
edge,  corresponding  to  the  dip  in  the  upper  surface  and 
making  what  is  known  as  "Phillips  entry",  is  not  advan- 
tageous. The  wing  shown  in  Fig.  14,  which  is  accurately 
drawn  to  scale,  has  a  more  effective  entry  than  the  wings 
sketched  in  Figs.  9  and  10. 

Incidence,  chord,  span  and  area  of  a  cambered  wing. 

A  wing  section,  or  side  view,  of  a  cambered  wing  is  shown 
in  Fig.  10.  The  chord  of  a  cambered  wing  is  a  straight  line, 
as  shown,  tangent  to  its  under  surface  at  front  and  rear. 


16 


AIRPLANE    CHARACTERISTICS 


The  length  of  chord  is  the  length  of  the  projection  ab  of  the 
wing-section  upon  this  chord.  Similarly,  the  area  of  a 
cambered  wing  is  its  area  projected  on  a  tangent  plane.  The 
span  or  spread  of  a  wing  is  the  maximum  distance  from  tip  to 
tip.  The  aspect  ratio  is  the  ratio  of  span  to  chord.  The 
angle  of  incidence  of  a  cambered  plane  is  the  angle  between 
its  chord  and  the  relative  air,  as  shown  in  the  same  figure. 


AIR 

STREAM 


ANGLE  COINCIDENCE 


Pig.  10.     Section  of  cambered  wing,  showing  angle  of  incidence 

between  the  chord  and  the  air-stream,  and  the 

components  of  pressure. 

Wing  structure. 

The  whole  wing  structure  is  often  referred  to  as  an  aerofoil. 
Wings  are  made  in  many  ways;  although  no  standard  con- 
struction can  be  shown,  the  one  shown  in  Fig.  loa  is  fairly 
typical.  Each  wing  is  commonly  built  up  of  two  spars,  as 
there  shown,  running  from  one  end  of  the  wing  to  the  other. 
Spars  may  be  of  I-beam  section,  double  I-beam,  box  con- 
struction, etc.  Supported  by  these  spars  are  the  ribs, 
extending  fore  and  aft,  each  rib  having  the  exact  shape  of  a 
wing-section.  The  top  and  bottom  of  each  rib  is  commonly 
made  of  strips  of  spruce,  held  in  place  and  strengthened  by  a 
thin  web,  which  gives  the  rib  an  I-beam  cross-section.  The 


SUSTENTAT10N  17 

web  is  partly  cut  away  for  lightness,  as  shown  in  the  illus- 
tration. 

The  camber  of  either  surface  of  a  wing  is  the  greatest  dis- 
tance between  the  chord  and  that  surface,  and  is  usually 
expressed  as  a  fraction  of  the  chord.  The  camber  of  the 
bottom  surface  indicated  in  Fig.  loa  is  about  i  /4o.  Mean 
camber  is  the  mean  between  the  top  camber  and  the  bottom 
camber. 

Components  of  pressure. 

The  pressure  P  is  considered  as  having  its  point  of  applica- 
tion at  the  point  0  where  it  intersects  the  chord  ab,  as  shown 


CAMBER 

BANGLE  OP  INCIDENCE 

Fig.  loa.    Wing  structure. 

in  Fig.  10.  This  point  is  called  the  center  of  wing  pressure 
and  is  located  (unless  the  incidence  is  very  small  or  negative, 
see  Fig.  13)  a  little  in  advance  of  the  middle  point  of  the 
chord. 

The  pressure  P  is  more  or  less  perpendicular*  to  the  chord. 
The  total  pressure  P  is  resolved  into  its  two  compon- 
ents, lift  L  and  wing-resistance  D,  which  also  have  their  point 
of  application  at  the  center  of  pressure  0.  The  direction  of  P 


*For  a  certain  angle  of  incidence  (when  cotangent  *  =  L/D),  P  coin- 
cides exactly  with  the  perpendicular  to  the  chord.  For  a  smaller  angle 
of  incidence,  P  is  back  of  the  perpendicular,  due  to  the  relatively  large 
value  of  D  compared  with  L.  For  a  larger  angle  of  incidence,  P  is  in 
advance  of  the  perpendicular,  due  to  the  relatively  larger  value  of  L. 


18 


AIRPLANE   CHARACTERISTICS 


can  be  determined  by  laying  off  L  and  D  where  these  are 
known;  P  =  \/U  +  D2.     In  ordinary  flight,  D  is  so  small 


MAXIMUM      LirT 

AT    BURBLE     POINT  !> 


.003 


ANGLE  OF  INCIDENCE 

Fig.  n.  Lift  and  wing-resistance  for  cambered  wing,  U.  S.  A.  5. 
Lift  (in  pounds)  =  K^SV2;  wing-resistance  (in  pounds)  =KDSV2, 
where  5  is  in  sq.  ft.  and  V  is  in  miles  per  hour.  For  wing-section, 
see  Fig.  14. 

compared  with  L,  as  shown  in  Fig.  n,  that  P  and  L  are 
practically  equal,  the  difference  being  less  than  one  per  cent. 


SUSTENTATION 


19 


Variation  of  lift  and  wing-resistance  with  angle  of  incidence 
of  a  cambered  plane. 

Each  different  wing-section  will  have  its  own  characteristic 
curves  for  lift  and  wing-resistance,  but  all  such  curves  have 


MAXIMUM 


ANGLE  OF  INCIDENCE  l 

Fig.  12.     Curves  for  L/D  ratio  and  D/L,  corresponding  to  Fig.  1 1. 

the  same  general  trend.  Fig.  n  shows  curves  for  the 
coefficient  of  lift  KL,  and  the  coefficient  of  wing-resistance 
£TD,  for  a  representative  cambered  wing,  designated  as 


20 


AIRPLANE   CHARACTERISTICS 


U.  S.  A.  5  and  shown  in  Fig.  14.  These  curves  are  typical 
and  will  serve  to  illustrate  certain  general  features  that  are 
characteristic  of  practically  all  cambered  wings. 

The  corresponding  values  for  the  L/D  ratio  (obtained  by 
dividing  KL  by  KD)  are  given  in  Fig.  12,  the  values  for  D /L 
being  shown  by  the  dotted  curve  in  the  same  figure. 

The  numerical  values*  from  which  these  curves  are  plotted 
are  given  in  Table  I. ;  these  values  will  be  used  in  later  cal- 
culations. 


TABLE  I.    WING  U.  S.  A.  5 


i 

KL 

K-D 

L/D 

C.P.f 

-4° 

—  .000326 

.OOOI5OO 

—  1.58 

—2° 

.000346 

.0000948 

3.64 

•753 

—  1° 

.000636 

.0000830 

7.67 

•566 

0° 

.000910 

.0000741 

12.28 

.498 

1° 

.001145 

.0000803 

14.28 

.444 

2° 

•001355 

.0000863 

1572 

.415 

3° 

.001565 

.0000966 

16.21 

•377 

4° 

.001740 

.OOOIO92 

15.98 

.348 

5° 

.001950 

.OOOI290 

15.35 

.337 

8° 

.002470 

.0001830 

13.52 

.315 

10° 

.002870 

.0002380 

12.08 

•303 

12° 

.003130 

.0002890 

10.84 

.300 

13° 

.003240 

.0003290 

9.84 

.298 

14° 

.003285 

•0003545 

9.25 

.288 

15° 

.003235 

.OOO39IO 

8.28 

.292 

16° 

.003205 

.OOO42IO 

7-63 

.298 

18° 

.003150 

.0006900 

4.57 

•330 

20° 

.002790 

.OOO82OO 

3-41 

•368 

tDistance  of  the  center  of  wing  pressure  from  the  leading  edge,  ex- 
pressed as  a  fractional  part  of  the  chord.  Shown  by  curve  in  Fig.  13. 

*From  tests  made  by  Captains  E.  S.  Gorrell  and  H.  S.  Martin, 
abstracted  by  A.  Kelmin  and  T.  H.  Huff;  published  in  Aviation,  Vol.  II., 
p.  256,  1917.  These  tests  were  made  on  a  model,  18"  x  3",  made  of 
brass;  density  of  standard  air:  0.07608  Ibs.  per  cu.  ft. ;  wind  velocity, 
30  MPH. 


SUSTENTATION  21 

Characteristic  features  of  a  cambered  wing. 

An  inspection  of  the  curves  in  Figs.  1 1  and  1 2  shows  the 
following : 

Lift  with  negative  incidence. — A  cambered  plane  exerts  a 
lift  even  at  a  small  negative  incidence.  Zero  lift  is  usually 
obtained  when  the  incidence  is  between  — 2°  and  — 4°  (in 
Fig.  ii  at  — 3°)  but  in  extreme  cases  the  incidence  may  be 
decreased  to  — 6°  or  — 8°  before  zero  lift  is  reached.  Although 
in  most  cases  an  airplane  flies  with  a  positive  incidence,  at 
high  velocities  it  may  fly  with  zero  incidence  or  with  a  small 
negative  incidence, — but  not  within  two  or  three  degrees  of 
the  point  of  zero  lift. 

In  approaching  the  point  of  zero  lift  there  is  danger  of 
going  too  far,  so  that  the  air  is  allowed  to  strike  the  top  sur- 
face of  the  wing,  causing  the  machine  to  take  a  nose  dive. 

Lift  is  a  maximum  at  about  14°. — As  the  incidence  is 
increased,  the  lift  increases  rather  uniformly  and  reaches  a 
maximum  of  more  than  0.003  at  an  incidence  of  14°  or  so, 
according  to  the  particular  wing.  The  angle  of  incidence 
at  which  K^  is  a  maximum  is  called  the  critical  angle.  Beyond 
this  maximum,  which  is  also  known  as  the  burble  point,  the 
lift  decreases  somewhat  irregularly  and  again  becomes  zero 
at  an  incidence  of  about  90°. 

Up  to  the  burble  point,  *.  #.,  for  an  incidence  of  less  than  14° 
or  so,  the  air-flow  past  the  wing  is  to  a  certain  extent  smooth 
and  without  eddies,  as  shown  in  Fig.  9.  Beyond  this  point, 
i.e.,  for  an  incidence  of  14°  to  90°,  there  is  a  confusion  of 
eddies  and  a  turbulance  (such  as  was  illustrated  in  Figs.  3 
and  5),  accompanied  by  a  decrease  in  lift  and  an  increase  in 
wing-resistance.  ("Burble"  means  "confuse;"  hence  the 
term  "burble  point.") 


22  AIRPLANE   CHARACTERISTICS 

Ususal  range  of  incidence  is  about  o°  to  10°. — It  is  seen  that 
the  lift  increases  more  or  less  uniformly  with  incidence,  from 
zero  lift  at  — 3°  to  maximum  lift  at  + 1 4°-  (It  is  to  be  under- 
stood that  other  wing-sections  would  give  slightly  different 
values.)  The  range  for  practical  flight  must  be  within  these 
limits,  without  either  limit  being  reached. 

The  lower  limit  of  zero  lift  cannot  be  reached,  inasmuch  as 
some  lift  is  necessary  for  sustentation ;  it  may  be  approached 
to  a  certain  extent  at  high  velocities,  but  too  near  an  approach 
may  lead  to  a  nose  dive  as  already  mentioned. 

The  upper  limit  of  maximum  lift  is  possible  but  in  ordinary 
flying  it,  too,  is  only  approached,  for  as  it  is  approached  there 
is  danger  of  a  stall  due  to  increase  of  wing-resistance,  leading 
to  a  fall  or  tail  slide.  With  the  decreased  velocity  which 
accompanies  increased  incidence,  the  stability  of  the  machine 
becomes  less  and  may  vanish  entirely;  as  the  power  of 
control  depends  upon  velocity,  the  recovery  of  equilibrium 
when  once  lost  at  low  speed  is  difficult.  Too  great  an 
incidence  is  a  frequent  cause  of  accident. 

Exact  limits*  can  not  well  be  set;  but,  roughly  speaking, 
the  range  of  incidence  is  between  o°  and  10°,  limits  which  are 
never  greatly  exceeded  in  ordinary  flight. 

(The  angle  of  incidence  may  be  increased  beyond  this 
limit — possibly  up  to  the  point  of  maximum  lift  f — as  a  machine 


"The  question  of  power  is  taken  up  later.  There  is,  for  each  machine, 
a  certain  angle  of  incidence — well  within  these  limits — at  which  the 
power  required  is  a  minimum.  If  the  incidence  is  either  increased  or 
decreased,  there  is  a  very  great  increase  in  the  amount  of  power  required. 

tAlthough  the  main  wing-surfaces  may  thus  in  some  cases  be  at  their 
maximum  lift,  the  surfaces  used  for  lateral  control,  called  ailerons  dis- 
cussed later,  should  always  be  well  below  maximum  lift.  Otherwise 
they  would  become  inoperative,  for  lateral  control  depends  upon  increas- 
ing the  lift  on  one  aileron  and  decreasing  the  lift  on  the  other;  if  the 
ailerons  were  at  maximum  lift,  any  change  would  decrease  the  lift  on 
both  and  would  not  give  the  desired  control. 


SUSTENTATION  23 

reaches  the  "ceiling,"  which  is  the  highest  possible  altitude 
a  particular  machine  can  attain ;  also,  when  slowing  down  to 
minimum  speed  just  prior  to  landing.) 

A  flat  maximum  in  the  lift  curve  is  very  desirable,  being 
less  dangerous  than  a  sharp  maximum  in  which  the  lift 
decreases  rapidly  after  the  critical  angle  is  reached.  A  flat 
maximum  is  more  readily  obtained  in  a  biplane  or  triplane — 
particularly  if  the  planes  are  staggered — than  in  a  monoplane 
for  the  maximum  points  for  the  separate  planes  may  not 
coincide,  so  that  when  the  separate  lifts  are  added  together 
to  get  the  total  lift  the  maximum  point  is  broadened  out. 

Wing-resistance  is  small  through  usual  range  of  incidence; 
then  increases  rapidly.—  Wing-resistance,  as  already  mentioned, 
is  in  no  case  zero.  It  is  small  throughout  the  useful  range  of 
incidence,  gradually  increasing  throughout  this  range  as  the 
incidence  increases.  As  the  incidence  is  further  increased,, 
the  wing-resistance  increases  a  little  more  rapidly  until  the; 
burble  point  or  point  of  maximum  lift  is  reached ;  after  which 
the  wing-resistance  increases  very  rapidly, — finally  reaching 
a  value  of  0.003  (more  or  less)  at  an  incidence  of  90°. 

LID  ratio  has  a  maximum  value  of  about  16  in  middle  range 
of  incidence. — If  the  wing-resistance  were  constant,  the  L/D 
ratio  would  be  a  maximum  when  the  lift  is  a  maximum.  On 
account  of  the  increase  in  wing-resistance  with  incidence,  the 
L/D  ratio  reaches  a  well  defined  maximum  before  the  maxi- 
mum lift  is  reached.  In  Fig.  1 2 ,  this  maximum  of  1 6. 2  occurs 
at  +3°.  This  is  a  good  value  for  L/D.  A  slightly  greater 
value,  17  or  18,  is  obtained  by  some  wings, — at  a  sacrifice 
perhaps  of  some  other  feature,  such  as  stability  or  ease  of 
construction. 

Comparison  with  flat  plane. — By  comparing  the  curves  in 
Figs,  ii  and  12  for  a  cambered  wing,  with  those  of  Figs.  6 


24 


AIRPLANE    CHARACTERISTICS 


and  7  for  a  flat  plane,  it  is  seen  that  the  cambered  plane  gives 
more  lift  (the  maximum  value  being  about  50  per  cent, 
more),  gives  less  wing-resistance  and  a  much  greater  L/D 
ratio, — nearly  three  times  as  great.  For  these  reasons  a 
cambered  wing  is  always  used. 


ENTERING  EDGE 


TRAILING  EDGE 


-5°'  •!(>«•  'IS* 

ANGLE  OF  INCIDENCE 


20° 


Fig.  13.     Position  of  center  of  pressure  on  a  cambered  wing 

(U.S.A.5.)  with  aspect  ratio  6,  for  different 

angles  of  incidence. 


Shifting  of  center  of  wing  pressure  with  incidence. 

The  position  of  the  center  of  pressure  for  the  cambered 
wing  in  question,  U.  S.  A.  5,  is  shown  in  Fig.  13.  All  cam- 
bered wings  show  a  marked  shifting  of  the  center  of  pressure 
toward  the  rear  of  the  plane,  when  the  incidence  is  small  and  is 
decreasing, — a  bad  feature  for  stability  as  discussed  in  a 
later  chapter. 


SUSTENTATION  25 

In  this  one  respect  a  cambered  wing  is  inferior  to  a  flat 
plane,  in  which  the  center  of  pressure  moves  forward  when 
the  incidence  is  decreasing,  as  shown  in  Fig.  8. 

The  shifting  of  the  center  of  pressure  shown  in  Fig.  13  is 
much  less  than  is  found  in  the  case  of  many  wings,  the  section 
of  wing  here  used  being  in  this  respect  satisfactory. 

Wing-section. 

There  is  no  one  type  of  wing  that  is  best.  The  particular 
wing,  to  which  all  the  curves  here  given  refer,  is  shown  in 
Fig.  14  and  is  fairly  representative.  But  it  will  be  under- 
stood that  in  different  machines  different  wings  may  best  be 


Fig.  14.     Section  of  wing,  U.S.A.  5. 


used,  according  to  the  particular  features  to  be  emphasized; 
high  speed  in  one,  large  load-carrying  capacity  in  another; 
stability  in  one,  quickness  in  maneuvering  in  another,  and 
so  forth. 

The  characteristics  of  any  particular  wing-section  are 
shown  by  means  of  curves,  such  as  those  shown  in  Figs,  n, 
12  and  13.  The  usefulness  of  these  curves  in  determining 
the  problems  of  flight  will  be  brought  out  in  the  following 
chapters. 

Comments  on  wing  sections. 

A  few  comments  on  wing  sections  may  here  be  made, 
although  the  reader  may  find  it  well  to  postpone  their  perusal 
until  he  has  read  some  of  the  subsequent  chapters  describing 
various  relations  and  characteristics  of  an  airplane  in  flight. 


26  AIRPLANE   CHARACTERISTICS 

Mechanical  as  well  as  aerodynamic  considerations  have  to  be 
kept  in  mind  by  the  designer ;  there  must  be  room  for  spars 
and  ribs  of  adequate  strength. 

For  climbing  and  for  heavy  lift,  a  wing  with  deep  camber 
(particularly  on  the  upper  surface)  and  large  value  of  K^ 
should  be  used.  For  this  purpose  a  deeply  cambered  wing  is 
flown  at  low  speed,  and  at  a  large  angle  of  incidence  as  shown 
in  Fig.  15.  Such  a  wing,  however,  is  utterly  unsuited  for 
flying  at  high  speed  and  small  incidence,  as  shown  in  Fig.  16, 
on  account  of  its  great  resistance  at  small  angles  of  incidence. 

For  speed,  the  wing  should  be  flatter  with  only  a  little 
camber,  with  less  lift  and  with  the  least  possible  wing- 
resistance  at  small  incidence  and  high  velocity.  It  is  neces- 
sary to  sacrifice  either  speed  or  lift.  A  speed  wing  is  sketched 
in  Fig.  17. 

Again,  both  speed  and  lift  may  be  sacrificed  for  stability. 
As  has  been  shown,  the  center  of  pressure  on  a  cambered 
wing,  convexed  upward,  shifts  with  change  of  incidence  (when 
the  angle  of  incidence  is  small)  in  the  wrong  direction  for 
stability.  If  a  cambered  wing  were  concave  downward — a 
very  bad  wing  for  lift — this  shifting  of  the  center  of  pressure 
would  be  in  the  right  direction  for  stability.  The  two  effects 
may  be  combined,  in  varying  proportions,  by  giving  a  wing 
a  double  curvature,  as  shown  in  Fig.  18.  In  this  case,  when 
the  machine  starts  to  dive  the  air  strikes  the  reversed  curve 
near  the  rear  of  the  wing  and  restores  equilibrium ;  but  this 
means  less  lift  and  more  resistance. 

The  characteristics  of  an  aerofoil,  although  in  a  general 
way  shown  by  its  section,  are  best  shown  by  curves  for  its 
performance,  as  in  Figs,  n,  12  and  13. 

A  high  maximum  to  the  K^  curve  is  of  no  advantage  in  a 
high  speed  machine  nor  in  ordinary  flight;  it  gives,  however, 


SUSTENTATION 


27 


the  ability  to  climb  to  high  altitudes  and  gives  a  low  landing 
speed,  as  brought  out  in  the  next  chapter. 

The  L  ID  curve  should  show  a  good  value,  not  necessarily 
a  maximum,  at  about  the  incidence  for  which  the  machine  is 
to  be  flown;  thus,  in  a  high  speed  machine,  it  is  desirable  to 
have  a  large  value  for  L  /D  at  a  very  small  incidence.  This  is 
only  another  way  of  saying  that  wing-resistance  D  should  be 
small. 


Fig.  15.  Wing  with  high  camber,  suitable 
for  big  lift  and  slow  speed,  when  blown 
at  large  angles  of  incidence  as  shown. 

Fig.  1 6.  Same  wing  at  small  incidence, 
entirely  unsuitable  for  high  speed  on 
account  of  large  wing-resistance  due  to 
its  camber. 

Fig.  17.  Flat,  stream-lined  wing  with 
little  camber  and  small  lift ;  suitable  for 
high  speed  on  account  of  its  very  small 
wing-resistance . 

Fig.  1 8.  Wing  with  reversed  curvature 
toward  trailing  edge  for  increased  sta- 
bility. This  is  paid  for  by  an  increase  in 
wing-resistance  and  a  decrease  in  lift. 


In  a  high  speed  machine,  which  is  to  be  flown  at  small 
incidence  and  at  small  K^,  it  is  desirable  to  have  a  curve  for 
KL  that  is  not  too  steep  as  it  approached  zero  lift;  thus,  it  is 
desirable  to  obtain  a  certain  lift,  when  the  plane,  let  us  say,  is 
3°  or  4°  rather  than  i°  or  2°  from  the  incidence  of  zero  lift. 
There  is  then  less  danger  of  a  nose  dive,  when  the  machine 
dips  a  little  as  it  oscillates  about  its  normal  direction  of  flight. 


CHAPTER  II 

RELATIONS   IN   FLIGHT 

Some  interesting  relations  in  regard  to  flight  can  be  drawn 
from  the  expressions  derived  in  the  preceding  pages  for  the 
lift  and  wing-resistance  of  a  cambered  plane.  In  this  chapter 
will  be  considered  the  significance  of  the  lift  equation,  and 
certain  relations  between  velocity  and  incidence  that  may  be 
derived  from  it;  wing-resistance  will  be  considered  in  the 
following  chapter. 

In  horizontal  flight,  weight  =  lift  =  KLSV2. 

We  have  seen  that  the  lift  that  supports  an  airplane  is 
equal  to  the  product  of  the  area  of  wing  5,  the  square  of  the 

LIFT 


WEIGHT 

Fig.  19.    Lift- weight  in  horizontal  flight. 

velocity  V,  and  a  coefficient  of  lift  KL  that  varies  with  the 
angle  of  incidence : 

Lift  =  L  =  KL  SV2. 

For  sustentation  in  horizontal  flight,  see  Fig.  19,  the  lift  must 
be  just  equal  to  the  weight  of  the  machine,  including  its  load ; 
we,  accordingly,  may  write 

Weight  =  W  =  KL  SV2. 
28 


RELATIONS  IN  FLIGHT  29 

Weight  acts  downward  through  the  center  of  gravity  or 
C.  G. ;  lift  acts  upward  through  the  center  of  lift  or  C.  L. 

These  two  centers  are  never  far  apart,  although  they  rarely 
coincide  exactly.  When  the  center  of  gravity  is  in  front  of 
the  center  of  lift,  there  is  a  moment  or  couple  tending  to  make 
the  machine  nose  down ;  when  the  center  of  gravity  is  back 
of  the  center  of  lift,  there  is  a  couple  tending  to  make  the 
machine  nose  up.  In  neither  case  does  the  couple  have  any 
affect  upon  the  value  of  weight  and  lift  (which  are  equal) , 
although  it  does  affect  longitudinal  stability. 

Velocity  equals  square  root  of  loading  divided  by  square 
root  of  KL. 

The    preceding    equation,    when    transposed,    gives    the 
important  formula  for  velocity, 


v  =  ^ik 


This  formula,  although  simple,  is  quite  complete  and  will 
bear  careful  study,  for  it  leads  to  a  number  of  interesting 
conclusions,  the  appreciation  of  which  is  essential  to  a  proper 
understanding  of  flight. 

The  ratio  W  /S  is  the  weight  per  unit  area  of  wing  and  is 
called  the  loading.  It  is  the  loading,  rather  than  weight  or 
area,  that  effects  the  value  of  V.  The  formula  shows  that 
the  velocity  of  an  airplane  depends  solely  upon  the  loading 
and  upon  KL. 

The  only  possible  way  for  changing  the  speed  of  a  machine, 
or  for  getting  different  speeds  in  different  machines,  is  by 
changing  the  loading  or  by  changing  the  value  of  KL.  In 
practice  there  are  of  course  limits  to  both  of  these  changes. 
For  a  machine  in  flight,  in  which  the  loading  can  not  be 


30 


AIRPLANE    CHARACTERISTICS 


changed,  the  only  way  for  changing  the  speed  is  by  changing 
the  value  of  K^. 

The  loading  W /S  is  commonly  about  6  Ibs.  per  sq.  ft., 
being  less  in  slow  machines  and  being  more  (8  and  even  10) 
in  fast  machines.  The  usual  limits  for  KL  are  about  0.0008 
and  0.003  2. 

This  gives  us  at  once  the  speed  variation,  shown  in  Fig.  20, 
for  any  machine  irrespective  of  wing-section  or  other  features 
of  design  except  loading.  Each  curve  in  Fig.  20  is  for  a 


K, 


..0016  .0020 

COEFFICIENT  OS1  LIJT 


Fig.  20.     Variation  of  velocity  with  coefficient  of  lift  for  any  airplane, 
when  loading  is  4,  6  (heavy  curve),  8  and  10. 

different  loading.  The  heavy  curve  shows  the  change  of 
speed,  with  KL,  for  a  machine  with  loading  W  /S  =  6,  this 
being  the  plot  of  the  equation  V  =  \/  6  -r-  KL.  The  light 
curves  are  for  loadings  4,  8,  and  10,  an  increase  in  loading 
raising  the  curve  and  thus  indicating  a  greater  velocity. 

It  is  seen  that  velocity  increases  as  KL  decreases;  if  KL 
were  zero,  V  would  have  to  be  infinite  to  create  a  lift  equal 
to  the  weight,  as  is  necessary  for  sustentation. 

Speed  range. — A  machine  that  has  a  maximum  speed  of 
100  miles  per  hour  and  a  minimum  speed  of  45  miles  per 
hour  is  said  to  have  a  speed  range  of  55  per  cent.  The  range 
in  speed  depends  upon  the  range  in  the  value  of  KL. 


RELATIONS  IN  FLIGHT  31 

Thus  it  is  seen  that,  if  we  take  the  limits  of  KL  as 
0.0008  and  0.0032,  the  speed  range  for  any  machine  is  fifty 
per  cent.  The  curves  in  Fig.  20  are  drawn  solid  between  these 
limits.  Commonly  the  speed  range  is  somewhat  less  than 
fifty  per  cent.,  but  in  some  cases  is  a  little  more.  (A  mini- 
mum value  of  KL  a  trifle  less  than  0.0008  may  be  attained  in 
some  instances;  but  a  greater  value,  0.0009  or  more,  is  per- 
haps a  more  usual  minimum.) 

By  way  of  illustration,  with  limits  0.0008  and  0.0032  for 
KL,  a  machine  with  loading  W  /S  =  10  would  have  speed 
limits  as  follows,  the  speed  range  being  50  per  cent. ; 


Maximum  speed  =\/10  •*•  0.0008  =  112  MPH. 
Minimum  speed  =-\A°  -=-  0.0032  =    56  MPH. 

As  a  further  illustration,  with  limits  0.00074  and  0.0034 
for  KL,  the  speed  range  would  be  about  54  per  cent. ;  thus, 


Maximum  speed  =\/io  -r-  0.00074  =  116  MPH. 
Minimum  speed  =  \/io  -f-  0.0034    =  54  MPH. 

The  speed  range  is  the  difference  between  maximum  and 
minimum  speed,  divided  by  the  maximum  speed;  thus,  in  this 
case,  speed  range  =  (116 — 54)  -s-  116  =  0.54  or  54  per  cent. 

A  greater  speed  can  be  attained  only  by  increasing  the 
loading  or  by  decreasing  KL.  For  example,  if  a  speed  of  200 
MPH.  is  to  be  attained:  W  /S  must  equal  29.6,  if  K^  — 
0.00074;  W  IS  must  equal  20,  if  K^  =  0.0005;  W  /S  must 
equal  10,  if  KL  —  0.00025;  etc. 

The  advantage  of  a  large  speed  range* — not  only  a  high 

*Some  early  machines  had  a  very  small  speed  range,  let  us  say  from  a 
minimum  of  35  to  maximum  of  50  miles  per  hour,  giving  a  speed  range 
of  1 5  miles  per  hour.  A  gust  from  behind  of  more  than  1 5  miles  per  hour 
would  reduce  the  relative  air  speed  below  the  requisite  35  miles  per  hour 
necessary  for  sustentation;  so  that  the  machine  had  no  support.  This 
was  one  cause  for  the  so-called  holes  in  the  air. 


32 


AIRPLANE   CHARACTERISTICS 


maximum  speed  for  flying  but  also  a  low  minimum  speed  for 
landing — is  obvious.  To  get  a  sufficiently  low  landing  speed 
is  one  of  the  problems  of  the  designer. 


.003 


.0025 


H  '.002 

& 

I-J 


s- 


0015 


g 


8  . 


.0005 


MINIMUM  VELOCITY 

MAXIMUM  LIFT 


4  2. 7  5  MILES  PER 
HOUR 


43.2 
MPH. 


8\.2  MPH. 
97.1    MPH. 
137.1  MPH. 


ANGLE  OF  INCIDENCE 

Fig.  21.     Variation  of  coefficient  of  lift  with  incidence  for  a  particular 

wing-section;  aspect  ratio  6.     Velocities  are  marked  for  several 

points,  assuming  a  loading  of  6  Ibs.  per  sq.  ft. 

A  given  machine  has  a  definite  velocity  for  each  angle  of 
incidence,  and  this  is  controlled  by  the  elevator. 

Since  KL  has  a  different  value  for  each  angle  of  incidence, 
it  is  seen  that  the  velocity  of  a  machine  varies  with  incidence 


RELATIONS  IN  FLIGHT  33 

and,  for  a  given  loading,  velocity  depends  only*  upon  incidence. 
The  angle  of  incidence  is  controlled  by  the  pilot  by  means  of 
the  elevator. 

The  variation  of  K^  with  incidence,  for  a  particular  wing- 
section,  is  shown  in  Fig.  21,  reproduced  from  Fig.  n  of  the 
preceding  chapter.  The  numerical  values  from  which  the 
curve  is  plotted  are  given  in  Table  I.,  page  20. 

For  any  given  loading,  the  values  of  V  corresponding  to  any 
point  on  this  curve  is  readily  determined.  For  example, 
suppose  W  JS  =  6.  For  an  incidence  of  4°,  from  the  curve 
or  table  K^  =  0.00174;  hence,  V  =\/6  -5-  0.00174  =  58.6 
miles  per  hour.  The  values  of  V,  determined  in  this  way, 
are  marked  for  several  points  on  the  curve.  It  is  seen  that 
for  each  incidence,  the  velocity  has  one  definite  value,  f 


*The  density  of  the  air  is  here  assumed  to  be  uniform;  see  a  later 
chapter  on  change  of  density  and  KL  with  altitude. 

t Modification  in  complete  machine. — The  lift  curve  for  a  wing  is  modi- 
fied in  a  complete  machine  by  whatever  lift  there  is  (either  positive  or 
negative)  on  other  parts  of  the  machine — body,  tail  and  other  surfaces — 
and,  in  a  biplane  or  triplane,  by  an  interference  between  the  planes  that 
reduces  the  lift.  This  reduction  is  less  when  the  gap  between  the  planes 
is  large  and  when  they  are  given  considerable  stagger  than  when  the 
gap  is  small  and  there  is  no  stagger.  Lift  likewise  increases  with 
aspect  ratio,  the  ratio  of  wing  span  to  chord.  For  the  curves  here 
shown  the  aspect  ratio  is  assumed  to  be  6,  the  usual  standard  value. 

For  simplicity  a  detailed  consideration  is  not  given  here  of  these 
features,  for  they  in  no  way  affect  the  general  character  of  the  conclu- 
sions, although  they  do  affect  the  precise  numerical  values.  Proper 
corrections  have  to  be  applied  when  exact  numerical  values  are  to  be 
obtained. 

The  net  result  of  these  corrections  usually  shifts  each  point  on  the 
lift  curve  a  little  to  the  right,  say  a  degree  or  so,  so  that  a  lift  K^  = 
0.00174  and  velocity  58.6  MPH.  shown  by  the  curve  at  4°  would,  for 
a  complete  machine,  be  at  say  5°,  and  so  on  for  other  points,  the  shift 
being  slightly  different  for  different  points.  So  far  as  lift  and  velocity 
are  concerned,  the  effect  of  these  corrections  is  merely  to  change  the 
angle  of  incidence  at  which  a  particular  value  of  lift  and  of  velocity 
occur.  Put  in  a  different  way,  at  small  angles  (perhaps  through  the 
working  range)  the  lift  curve  is  somewhat  lowered  and  at  large  angles  is 


34  AIRPLANE   CHARACTERISTICS 

Minimum  velocity  occurs  at   the  point  of   maximum  KL, 
namely  at  the  critical  angle  of  incidence  or  burble  point. 

It  is  seen  that  the  minimum  velocity  occurs  when  the  value 
of  KL  is  a  maximum,  namely  at  the  critical  angle  of  incidence 
or  burble  point.  For  any  other  incidence,  KL  is  less  and  V  is 
correspondingly  greater;  in  other  words,  when  the  angle  of 
incidence  is  either  greater  or  less  than  the  critical  angle,  a 
greater  velocity  is  required  in  order  to  produce  the  lift  equal  to 
the  weight,  the  condition  necessary  for  horizontal  flight. 

Variation  of  velocity  with  incidence. 

The  variation  of  velocity  with  incidence  is  well  shown  by 
the  curves  in  Fig.  22,  which  correspond  to  Fig.  21  and  refer, 
therefore,  to  a  particular  wing-section, — not  to  any  wing- 
section  as  was  the  case  in  Fig.  20.  Curves  for  the  variation 
of  velocity  with  incidence  for  other  wing-sections  would  have 
much  the  same  general  form. 

The  heavy  curve  in  Fig.  22  shows  the  velocity  for  a  loading 
W IS  =  6;  the  light  curves,  for  loadings  of  4  and  8, — the 
greater  loading  always  corresponding  to  the  higher  velocity. 

It  is  seen  that  there  is  a  definite  minimum  velocity  which 
occurs  at  the  critical  angle  of  incidence — in  this  case  14°— 
when  KL  is  a  maximum,  as  was  also  shown  in  Fig.  21.  If  a 
machine  loses  velocity  below  this  minimum,  it  cannot  sustain 
itself  and  is  said  to  stall, — the  critical  angle  of  incidence  being 
also  called  the  stalling  angle. 


somewhat  raised, — for  at  large  angles  the  lift  of  the  airplane  body 
becomes  effective. 

The  lift  curve  for  a  complete  machine  may  be  determined  by  applying 
proper  corrections  to  the  lift  curve  for  the  wing  (which  is  of  course  the 
chief  factor)  when  data  for  these  corrections  is  available;  but  it  is  best 
determined  by  a  wind-tunnel  test  with  a  complete  model.  Some  of  these 
corrections  are  to  be  considered  later  in  the  chapter  on  Single  and 
Multiple  Planes. 


RELATIONS  IN  FLIGHT 


35 


The  velocity  increases  on  each  side  of  this  minimum,  with 
change  of  incidence,  so  as  to  furnish  the  necessary  sustenta- 


140 


100 
80 
60 
40 
20 
10 


85 

*t 

h 


-5e  0°  5°  i(J»  15°  20° 

ANGLE  OF  INCIDENCE 

Fig.  22.     Variation  of  velocity  with  angle  of  incidence  for  particular 

wing-section,  when  loading  is  4,  6  (heavy  curve)  and  8.     These 

curves  correspond  to  the  curve  in  Fig.  21. 

tion,  and  would  have  to  be  infinite  were  K^  equal  to  zero, 
namely  if  the  incidence  were  decreased  (in  this  case)  to  —  3° 
or  were  increased  to  about  90°;  but,  as  already  pointed  out, 
there  are  limits  to  the  working  range  of  incidence  and  velocity. 


Usual  working  range. 

Between  the  limits  of  o°  and  10°  (corresponding  to  KI,  = 
0.00091  and  KL  =  0.00287)  the  curves  are  drawn  as  solid 
lines;  these  limits  would  become  -^3°  and  i2>£°,  if  the 
limits  of  KL  were  taken  as  0.0008  and  0.0032  as  before.  (It 
is  understood  that  precise  limits  cannot  be  set.)  This  shows 
the  usual  working  range :  two  or  three  degrees  less  incidence 
would  cause  a  dive;  two  or  three  degrees  more  incidence 


36  AIRPLANE   CHARACTERISTICS 

would  cause  a  stall.  An  inclinometer  is  commonly  used  to 
indicate  the  degrees  angle  of  incidence  (usually  by  a  bubble) 
and  the  advantage  of  its  use  is  obvious.  A  stall  indicator  is 
less  frequently  used  to  display  a  danger  signal  when  the 
stalling  angle  is  approached. 

Possibility  of  changeable  wing-area  or  camber. 

For  mechanical  reasons,  wings  are  made  with  fixed  area 
and  camber.  A  practical  wing  with  either  of  these  adjusta- 
ble would  do  much  to  advance  the  art  of  flying,  for  it  would 
make  possible  a  great  increase  in  speed  range,  both  by  increas- 
ing the  maximum  and  decreasing  the  minimum  speed.  These 
improvements  have  long  been  considered,  the  adjustable 
camber  now  seeming  the  more  promising  of  the  two. 

With  adjustable  wing-area,  the  pilot  would  use  large  area 
for  low  speed  and  would  use  small  area  for  high  speed. 

With  adjustable  camber,  the  pilot  would  use  for  low  speed 
such  camber  as  gave  maximum  lift.  For  high  speed  he 
would  flatten  out  the  wing  and  so  get  less  lift  without  a 
dangerous  reduction  in  incidence.  This  flattening  of  the 
wing  would  also  bring  about  a  reduction  of  wing-resistance, — 
a  highly  important  advantage  at  high  speeds. 

For  the  present,  however,  it  is  necessary  to  be  content  with 
wings  of  fixed  area  and  camber. 

Power  has  no  direct  effect  upon  velocity. 

It  has  been  shown  that  the  velocity  of  a  machine  is  depend- 
ent only  upon  incidence  (ignoring  the  possibility  of  a  change 
in  wing-area  or  camber  and  the  effect  of  altitude) ,  incidence 
being  controlled  by  the  position  of  the  elevator.  It  may  well 
be  asked:  What  about  power?  What  effect  upon  velocity 
has  the  amount  of  power  supplied  by  the  engine?  The 


RELATIONS  IN  FLIGHT  37 

answer  is :  The  power  supplied  by  the  engine  has  no  direct 
effect  upon  velocity,  whatsoever;  if  the  elevator  is  kept  in 
one  position  without  change,  the  same  angle  of  incidence  is 
maintained,  and  hence  the  same  velocity,  irrespective  of  the 
power  supplied  by  the  engine.  The  effect  of  power  is 
shown  in  the  following  paragraphs. 

Let  us  suppose,  for  example,  a  machine  is  flying  with  a 
certain  angle  of  incidence — say,  4° — determined  by  the 
position  of  the  elevator.  The  velocity  of  flight  is  then 
definite, — 58.6  MPH.,  if  we  use  the  data  in  Fig.  21.  At  a 
definite  velocity  and  incidence,  the  resistance  of  the  airplane 
(structure  as  well  as  wings)  is  definite — in  a  certain  instance 
263  Ibs. — to  overcome  which  there  must  be  an  exactly  equal 
thrust  (263  Ibs.)  requiring  the  supply  of  a  certain  amount  of 
power  (in  this  instance  42  horse  power).  But  this  definite 
amount  of  power  that  is  required  may  or  may  not  be  supplied 
by  the  engine,  for  this  depends  on  the  throttle.  Let  us  see 
what  happens  when  the  engine  does  not  supply  this  amount 
of  power. 

Amount  of  power  supplied  by  engine  determines  whether 
machine  climbs,  glides  or  flies  horizontally;  but,  if  inci- 
dence is  not  changed,  does  not  affect  velocity. 

If  the  engine  supplies  just  the  right  amount  of  power 
required  to  overcome  the  total  air  resistance,  the  machine 
flies  horizontally,  as  in  Fig.  23.  If  it  supplies  more  power, 
the  machine  takes  an  oblique  path  upward,  as  in  Fig.  24,  the 
"surplus  power"  being  used  against  gravity.  If  the  engine 
supplies  less  power  than  is  necessary  to  overcome  resistance, 
the  machine  takes  an  oblique  path  downward,  as  in  Fig.  25, 
the  necessary  additional  power  being  in  this  case  supplied  by 
gravity. 


38  AIRPLANE    CHARACTERISTICS 

Thus,  if  the  power  required  to  overcome  the  total  air 
resistance  is  42  H.P.,  there  are  the  three  cases:  when  the 
engine  delivers*  42  H.P.,  flight  is  horizontal;  when  it  delivers 


AIR  : 

5TREAM- 


G  FLIGHT   PATH 

Fig.  23.     Horizontal  flight. 

more  power,  47  H.P.  for  example,  the  machine  climbs,  auto- 
matically taking  a  flight  path  inclined  upward  at  such  an 
angle  that  the  surplus  5  H.P.  is  used  in  overcoming  gravity; 
when  the  engine  delivers  37  H.P.,  the  machine  takes  an 
oblique  path  downward  at  such  angle  that  5  H.P.  is  derived 
from  gravity.  The  angle  of  incidence — the  angle  between 
the  chord  and  the  relative  air  or  flight  path — being  the  same 
in  the  three  cases,  the  velocity  is  the  same  irrespective  of 
whether  the  flight  path  is  horizontal  or  oblique. 


FLIGHT  PATH 


Fig.  24.     Oblique  flight,  upward.     The  same  incidence 
and  speed  as  in  Fig.  23. 

It  is  seen  that  if  the  power  is  increased  or  decreased,  by 
adjustment  of  the  throttle,  the  inclination  of  the  flight-path  is 
changed,  but  (provided  the  elevator  is  not  changed)  the  angle 
of  incidence  and  velocity  remain  unchanged.  Indeed,  if  the 
power  is  entirely  cut  off,  the  machine  takes  an  oblique 


The  power  available  for  producing  thrust,  delivered  through 
the  propeller,  is  here  referred  to.  The  question  of  propeller  efficiency 
is  not  here  taken  into  consideration. 


RELATIONS  IN  FLIGHT  39 

flight-path  downward  at  a  definite  gliding  angle,  while  the 
velocity  still  remains  unchanged.  These  relations  will  be 
more  fully  discussed  in  subsequent  chapters  on  Climbing  and 
Gliding. 

When  horizontal  flight  is  to  be  maintained,  velocity  is 
changed  by  a  simultaneous  adjustment  of  throttle  and 
elevator. 

From  the  foregoing,  it  is  seen  that  the  one  way  to  change 
velocity  is  to  change  the  angle  of  incidence  by  means  of  the 
elevator ;  furthermore,  if  horizontal  flight  is  to  be  maintained, 
the  throttle  must  be  adjusted  at  the  same  time  so  that  the 
amount  of  power  required  for  horizontal  flight  is  supplied  by 
the  engine, — otherwise  the  flight  path  will  be  oblique.  The 
pilot  does  not  speed  up  and  go  faster  merely  by  opening  and 
closing  the  throttle,  as  in  an  automobile.  As  a  matter  of 


Fig.  25.     Oblique  flight,  downward.     The  same  incidence 
and  speed  as  in  Figs.  23  and  24. 

fact  an  airplane  is,  in  normal  flight,  practically  a  constant 
speed  machine,  flying  usually  at  the  one  velocity  correspond- 
ing to  a  certain  best  angle  of  incidence  for  which  the  machine 
is  designed. 

It  takes  more  power  to  fly  at  low  speed  or  at  high  speed 
than  at  an  intermediate  speed.  The  amount  of  power 
required  to  maintain  horizontal  flight,  as  shown  in  a  later 
chapter,  increases  very  rapidly  when  the  velocity  is  either 
increased  or  decreased  beyond  a  rather  narrow  range.  Power 


40  AIRPLANE  CHARACTERISTICS 

as  well  as  stability  is,  accordingly,  a  factor — in  many  cases  a 
determining  factor — in  deciding  the  range  of  velocity  and  the 
limiting  values  for  the  angle  of  incidence  and  for  KL. 

To  find  out  how  much  power  is  necessary  for  horizontal 
flight,  we  must  first  know  the  thrust  and  this  is  determined 
by  the  total  resistance  that  is  to  be  overcome.  This  will, 
accordingly,  be  next  investigated. 


CHAPTER   III 

RESISTANCE 

Resistance  is  the  force  that  impedes  the  progress  of  an 
airplane  through  the  air,  this  force  being  in  the  same  direction 
as  the  air-stream,  and  opposite  to  the  direction  of  flight,  as 


THRUST 


RESISTANCE 


Fig.  26.     Resistance  is  in  direction  of  the  air-stream 
and  is  overcome  by  thrust. 

shown  in  Fig.  26.     Resistance  is  overcome  by  thrust  from  the 
propeller,  a  force  in  the  direction  of  flight,  or  nearly*  so. 

In  uniform  flight  a  machine  assumes  such  a  velocity  and 
attitude  that  resistance  and  thrust  are  exactly  equal. 

Center  of  resistance. 

Thrust  is  a  force  forward  through  the  propeller  shaft, 
applied  at  the  center  of  thrust  or  C.  T.  The  total  resistance 
of  an  airplane,  the  resistance  of  wings  and  structure  all 
included,  may  be  considered  as  a  single  force  backward  in 
the  direction  of  the  air-stream  applied  at  the  center  of  resist- 
ance or  C.  R.,  which  may  coincide  with  the  center  of  thrust  as 
in  Fig.  26,  or  may  be  a  little  above  or  below  it.  When  the 


*When  thrust  is  inclined  with  reference  to  the  flight  path,  resistance  is 
overcome  by  the  component  of  thrust  in  the  direction  of  the  flight  path. 
The  small  vertical  component,  when  upward,  supports  part  of  the 
weight  so  that  correspondingly  less  lift  is  required  of  the  wing  for 
sustentation;  when  downward,  correspondingly  more  lift  is  required. 

41 


42  AIRPLANE   CHARACTERISTICS 

center  of  resistance  is  above  the  center  of  thrust,  there  is  a 
tendency  for  the  machine  to  nose  up  when  power  is  on,  and 
when  the  center  of  resistance  is  below  the  center  of  thrust 
there  is  a  tendency  for  it  to  nose  down.  This  affects  longi- 
tudinal stability  but  in  no  way  affects  the  value  of  resistance 
or  thrust. 

Wing-resistance  and  parasite  resistance. 

Airplane  resistance  falls  under  two  heads:  wing-resis- 
tance, due  to  the  wings;  and  parasite  resistance,  due  to  all 
other  parts  of  the  airplane  structure.  (Parasite  resistance  is 
sometimes  called  "structural  resistance"  or  "head  resist- 
ance.") The  sum  of  the  two  is  the  total  resistance  or  drag; 
thus, 

Total  Resist.  =  Wing  Resistance  +  Parasite  Resistance. 
In  English  units,  resistance  is  expressed  in  pounds. 

Although  expressed  by  very  similar  fundamental  formulas, 
each  varying  as  the  square  of  the  velocity,  wing-resistance  and 
parasite  resistance  have  quite  different  characteristics: — 
wing-resistance  depends  upon  incidence,  the  variation  of  the 
coefficient  of  wing-resistance  K^  with  incidence  having  been 
shown  in  Fig.  n,  page  18,  of  the  first  chapter;  parasite 
resistance,  on  the  other  hand,  is  practically  independent  of 
incidence,  except  so  far  as  incidence  affects  velocity. 

Whereas  parasite  resistance  always  increases  as  velocity  is 
increased,  wing-resistance  decreases  as  velocity  is  increased 
until  a  certain  velocity  is  reached,  after  which  it  increases,  as 
brought  out  in  the  following  discussion. 

On  account  of  their  different  characteristics,  wing-resistance 
and  parasite  resistance  are  considered  separately. 


RESISTANCE  43 

WING  RESISTANCE 
Fundamental  relation. 

Wing-resistance  is  equal  to  KnSV2,  as  shown  in  the  first 
Chapter,  and  is  fundamentally  determined  by  this  formula. 
A  hasty  inspection  of  the  formula,  however,  might  lead  to 
the  erroneous  conclusion  that  wing-resistance  always  increases 
with  velocity.  This  indeed  would  be  true,  if  KD  were  con- 
stant; but  in  fact,  as  mentioned  above,  the  changes  in  the 
value  of  KD  with  incidence  actually  cause  wing-resistance 
to  decrease  through  a  certain  range  of  velocities,  and  then  to 
increase  at  high  velocities.  This  is  best  shown  by  some 
practical  calculations  and  the  plotting  of  curves. 

Practical  calculation. 

Wing-resistance  can  be  calculated  directly  from  the  formula 
KvSV".  The  calculation,  however,  can  be  made  more  readily 
from  the  L  JD  ratio  for  the  particular  wing  in  question.  By 
definition 

L  ID  ratio  =  Lift  -r-  Wing-resistance. 
Since  Lift  =  Weight,  in  horizontal  flight,  we  may  write 
Wing-resistance*  =  Weight  -j-  L  /D  ratio. 

To  get  the  wing  resistance,  it  is  merely  necessary  to  divide 
the  known  weight  by  the  L/D  ratio,  the  value  of  this  ratio 
being  taken  from  a  table  or  curve  for  the  particular  wing 
section. 


*  Variation  of  wing-resistance  with  incidence. — The  formula  given  above 
may  also  be  written: — 

Wing-resistance  =  Weight  x  D/L  ratio. 

Wing-resistance  is,  therefore,  proportional  to  D/L.  A  curve  giving 
the  values  for  wing-resistance  for  different  angles  of  incidence  would 
be  similar  to  the  D/L  curve,  Fig.  12,  page  19,  the  only  difference  between 
the  two  curves  being  the  scale. 


44  AIRPLANE   CHARACTERISTICS 

Example.  —  For  example,  the  weight  of  a  loaded  machine  is 
2000  Ibs.  The  values  for  the  L  /D  ratio  for  the  wing  used  are 
given  by  the  Table  I.,  page  20,  or  by  the  corresponding  curve, 
Fig.  12,  page  19.  Required  to  find  the  wing-resistance  and 
velocity  for  an  incidence  of  4°.  From  the  table,  L/D  =  16 
(approximately);  hence 

Wing-resistance  =  2000  -f-  16  =  125  Ibs. 

It  is  seen  that  every  16  Ibs.  of  weight  adds  one  pound  to 
the  wing-resistance  and  will  require  one  pound  more  thrust, 
and  a  corresponding  increase  in  power,  to  overcome  it. 

To  determine  the  velocity  corresponding  to  the  wing- 
resistance  in  the  above  example,  it  is  necessary  to  know  the 
loading,  for  velocity  depends  upon  loading.  Thus,  if  the 
loading  is  W  /S  =  6  Ibs.  per  sq.  ft.,  using  the  formula  of  the 
preceding  chapter,  we  have 


\w~     .  - 

=  x  /  —  =  \/6  -r-  0.00174  =  58.6  MPH. 
V«3*vL 


Velocity 

It  is  thus  seen  that  when  this  particular  wing-section  is 
used  in  a  machine  weighing  2000  Ibs.,  with  loading  6  Ibs.  per 
sq.  ft.,  the  wing-resistance  is  125  Ibs.  at  a  velocity  of  58.6 
MPH. 

Variation  of  wing-resistance  with  velocity. 

The  variation  of  wing-resistance  with  velocity  is  well  shown 
by  the  curves  in  Figs.  27,  28,  and  29,  the  points  being 
calculated,  in  the  manner  just  described,  for  different  condi- 
tions of  weight  and  loading. 

It  is  seen  that  with  increase  of  velocity  (decrease  of  inci- 
dence) wing-resistance  always  decreases  until  a  certain 
velocity  is  reached,  after  which  it  again  increases.  The 
minimum  velocity  for  any  wing-section  is  obtained  at  the 
critical  angle  of  incidence;  a  greater  angle  of  incidence  is 


RESISTANCE 


45 


beyond  the  range  of  practical  flight.  The  critical  angle  for 
the  particular  wing-section  here  used  is  14°,  but  the  curves 
have  been  calculated  beyond  14°  in  some  instances  and  are 
shown  by  dotted  lines. 


350 


2,0 


100 
100 


OS 
O 


14-  « 


20  ^0  60  8Q  iOO 

VELOCITY  -  -  MILES  PER  HOUR 

Fig.  27.  Variation  of  wing-resistance  with  velocity. 
The  three  curves  show  effect  of  changing  weight 
(W  =  1000,  2000  and  3000  Ibs.)  when  loading  is  kept 
constant  (W/S  =  6). 


As  incidence  is  decreased  to  o°,  -i°,  -2°,  etc.,  wing-resis- 
tance and  velocity  both  rapidly  increase  and  both  would 
become  infinite  at  the  incidence  that  gives  zero  lift, — in  this 
case  at  -3°. 

Effect  of  changing  weight  or  loading. 

In  calculating  the  curves  here  shown,  it  was  necessary  to 
know  the  weight  and  loading, — inasmuch  as  wing-resistance 
=  weight  -T-  L/D,  and  velocity  =\/\oa.dmg  -5-  KL.  Dif- 
ferent curves  for  the  variation  of  wing-resistance  with 
velocity  are  accordingly  obtained  by  changing  either  weight 
or  loading,  or  both,  and  in  no  other  way, — it  being  understood 
that  we  are  dealing  with  a  particular  wing-section  flying  in 


46 


AIRPLANE    CHARACTERISTICS 


350_ 
I 
j 

|3CQ 

> 

"250 


jurf. 
100 


g» 

^       0 


so  40  do  BO  ioa 

VELOCITY  -  -    MILES  PER  HOUR 


Fig.  28.  Variation  of  wing-resistance  with  velocity.  The 
three  curves  show  effect  of  changing  loading  ( W/S  =  4,  6 
and  8)  when  weight  is  kept  constant  (W  =  2000  Ibs.). 


350 


300 


j     2ftO 
I 

S*oo 
&5XSO 

gioo 

O     50 


£666 


^..---      VV=I33J 


0  20  40  60  80  100 

VELOCITY    -  -  MILES  PER  HOUR 

Fig.  29.  Variation  of  wing-resistance  with  velocity.  The 
three  curves  show  effect  of  changing  weight  (W  =  1333. 
2000  and  2666  Ibs.)  and  loading  (W/S  =  4,6  and  8)  in 
proportion,  wing-area  being  constant. 


RESISTANCE  47 

air  of  constant  density.     It  will  be  found  that  all  the  curves 
are  similar  in  form  and  differ  only  in  scale. 
There  are  three  cases: 

(1)  when  weight  is  changed  and  loading  is  kept   constant; 

(2)  when  loading  is  changed  and  weight  is  kept  constant; 

(3)  when  weight  and  loadmg  are  both  changed. 

(1)  Effect  of  changing  weight  when  loading  is  kept  constant. 

In  this  case  machines  with  greater  weight  also  have  greater 
wing  area,  the  loading  remaining  constant.  Wing-resistance 
for  different  machines  is  then  directly  proportional  to  weight. 
This  is  shown  by  the  curves  in  Fig.  2  7  for  three  machines  of 
different  weight.  Any  point  on  these  curves,  corresponding 
to  a  particular  incidence  and  velocity,  is  merely  moved  up  for 
a  heavier,  or  down  for  a  lighter,  weight  machine ;  the  heavier 
the  machine,  the  greater  is  the  wing-resistance. 

(2)  Effect  of  changing  loading  when  weight  is  kept  constant. 

In  this  case  weight  is  constant  and  wing-area  is  changed  so 
as  to  give  different  loadings.  Changing  the  loading,  for  a 
certain  weight,  changes  the  velocity  corresponding  to  a  cer- 
tain incidence,  but  does  not  change  the  amount  of  wing- 
resistance,  for  that  incidence.  Hence,  as  shown  by  the 
curves  in  Fig.  28,  a  change  of  loading  shifts  to  right  or  to  left 
the  point  corresponding  to  a  particular  angle  of  incidence,  the 
velocity  for  that  incidence  being  proportional  to  the  square 
root  of  the  loading. 

The  loading  which  gives  the  least  wing-resistance  is  differ- 
ent at  different  velocities.  Thus,  for  the  case  shown  by  the 
three  curves  in  Fig.  28  with  loading  4,  6  and  8,  up  to  about  55 
miles  per  hour  the  wing-resistance  is  least  for  a  loading  of  4 ; 
from  55  to  65  miles  per  hour,  for  a  loading  of  6 ;  and  above  65 
miles  per  hour,  for  a  loading  of  8. 


48  AIRPLANE    CHARACTERISTICS 

(3)  Effect  of  changing  both  weight  and  loading,  wing-area 
being  constant. 

This  is  a  combination  of  the  two  preceding  cases.  A  point 
on  any  of  the  curves  is  moved  up  or  down  in  proportion  to 
weight,  and  to  right  or  left  in  proportion  to  the  square  root 
of  the  loading. 

The  three  curves  in  Fig.  29  show  the  effect  of  changing 
weight  and  loading  in  proportion,  wing-area  remaining  con- 
stant; this  might  be  brought  about  by  taking  up  the  same 
machine  at  different  times  with  different  loads.  It  is  to  be 
noted  that,  at  the  same  angle  of  incidence,  greater  velocity 
is  required  to  sustain  the  greater  weight;  or,  at  the  same 
velocity,  a  greater  angle  of  incidence  is  required. 

Variation  of  wing-section. 

For  a  given  wing-section  there  are  the  three  possible  ways 
just  described  for  changing  wing-resistance, — by  changing 
the  weight,  the  loading  or  both.  If  the  wing-section  is  varied, 
the  number  of  possible  variations  is  infinite.  A  wing  that  has 
high  camber  in  order  to  secure  great  lift,  also  has  large  resis- 
tance, particularly,  at  small  angles  of  incidence;  while,  as 
already  mentioned,  a  flatter  wing  with  less  camber  and  less 
lift  is  better  adapted  for  high  speed,  having  small  resistance. 
But  there  are  many  intermediate  forms  and  variations  that 
make  an  interesting  field  for  study. 

PARASITE  RESISTANCE 
Meaning  and  importance  of  parasite  resistance. 

The  wings  of  an  airplane  are  its  first  essential,  for  they 
create  the  lift,  but  in  creating  lift  they  at  the  same  time  cause 
a  wing-resistance.  Wing-resistance,  therefore,  although  not 
a  cause  of  lift,  is  seen  to  be  a  necessary  concomitant  being 


RESISTANCE 


49 


the  price  paid  for  the  lift.  In  a  preceding  example,  it  was 
shown  that,  in  a  given  case,  every  sixteen  pounds  of  lift  must 
be  paid  for  by  one  pound  of  wing-resistance. 

Unfortunately  this  is  not  all.  In  addition  to  wings  an 
airplane  must  have  other  parts — body,  landing  gear,  struts, 
wires,  etc., — all  of  which  have  a  resistance;  but  unlike  the 
wings,  these  parts  do  not  contribute  to  the  lift.  The 
resistance  of  these  parts  is,  therefore,  with  some  appropri- 
ateness called  parasite  resistance. 

One  of  the  important  problems  in  design  is  to  make  this 
parasite  resistance  as  low  as  possible,  for  while  small  at  low 


Fig.  30.     Air-flow  past  a  cylindrical  strut ;  air  eddies  and 
low  pressure  back  of  strut  cause  high  resistance. 

velocities  parasite  resistance  is  very  great  at  high  velocities, 
being  perhaps  fifty  per  cent,  more  than  wing-resistance  at 
ordinary  maximum  flying  velocities.  In  airplane  flight,  while 
about  two-fifths  of  the  power  delivered  through  the  propeller 
by  the  engine  is  used  in  pushing  the  wings  through  the  air, 
three-fifths  of  the  power,  approximately,  is  used  up  in  para- 
site resistance.  It  is  seen  that  parasite  resistance  is  the 
biggest  obstacle  to  high-speed  flight. 

Streamline  flow. 

Fig.  30  shows  the  flow  of  air  past  a  cylindrical  strut  or  wire. 
Behind  the  strut  there  is  a  turbulent  space  and  a  partial 
vacuum,  or  negative  pressure  n,  that  tends  to  suck  the  strut 


50  AIRPLANE  CHARACTERISTICS 

along  in  the  direction  of  the  air-stream.  A  large  part  of  the 
resistance  of  the  strut  to  motion  through  the  air  is  thus  due 
to^'this  region  of  low  pressure  behind  it. 

In  Fig.  31,  the  space  behind  the  cylindrical  strut  A  is 
partly  filled  by  a  piece  B,  so  as  to  reduce  the  region  of  tur- 


Fig.  31.  Cylindrical  strut  A,  backed  up  by  a  filler  B  of 
a  form  that  reduces,  but  does  not  entirely  eliminate, 
the  air  eddies  and  low  pressure  back  of  strut.  Resist- 
ance is  thus  reduced. 

bulence  and  low  pressure.  The  resistance  to  motion  through 
the  air  is  thus  greatly  decreased.  Struts  are  sometimes  made 
in  this  manner,  a  piece  A  for  strength  being  backed  up  by  a 
piece  B,  of  light  material  to  save  weight,  and  resistance  may 
be  reduced  in  this  way. 

Although  the  shape  shown  in  Fig.  3 1  is  an  improvement  on 
the  cylindrical  strut,  it  is  by  no  means  the  best,  for  it  does  not 


Fig.  32.     Strut  with  air  eddies  and  low  pressure  back  of 

strut  further  reduced,  by  approaching 

a  streamline  form. 

conform  entirely  to  the  streamline  flow ;  there  is  still  a  turbu- 
lent region  n,  although  this  is  much  reduced.     The  more 


RESISTANCE  51 

nearly  a  body  conforms  to  streamline  flow  the  less  is  its 
resistance,  the  turbulence  and  suction  back  of  the  body  being 
then  reduced  to  a  minimum.  Fig.  32  shows  a  strut  more 
nearly  conforming  to  streamline  flow. 

Only  a  little  is  gained  by  tapering  the  front  side  of  a  cylinder 
or  strut.  Note  the  blunt  breast  and  tapering  tail  of  a  bird, 
and  the  shape  of  a  fast  swimming  fish  that  can  dart  through 
the  water  with  scarcely  a  ripple. 

For  low  resistance,  wheels  and  body  should  be  enclosed; 
these,  as  well  as  every  strut  and  wire,  should  be  streamlined 
so  far  as  they  can  be.  It  should  be  remembered  that  a  small 
cylindrical  wire  may  offer  much  more  resistance  than  a  larger 
wire  that  is  well  streamlined. 

Parasite  resistance  varies  as  the  square  of  the  velocity. 

The  law  for  parasite  resistance  is  summed  up  in  the  state- 
ment, determined  by  experiment,  that  parasite  resistance 
varies  as  the  square  of  the  velocity.  This  applies  not 
only  to  the  separate  parts*  but  also  to  an  airplane  as  a  whole. 
Thus,  if  a  certain  airplane  has  a  parasite  resistance  of  64 
pounds  when  flying  at  40  miles  per  hour,  it  will  have  a 
resistance  of  256  pounds  at  80  miles  per  hour.  In  this  case 
the  parasite  resistance  is  o.o^V2. 

The  curves  in  Fig.  33  show  the  values  for  parasite  resistance 
at  different  velocities  for  three  cases,  R  =  0.02V2,  R  = 


"There  is  an  appreciable  departure  from  the  square  law  when  the 
skin  resistance  of  a  body  is  large  compared  with  the  direct  impact  or 
dynamic  resistance — the  more  so  when  the  surface  is  rough  and  the  f ore- 
atid-aft  dimension  of  the  body  is  large  in  proportion  to  the  diameter — 
but  practically  it  is  simplest  to  neglect  this  and  to  assume  the  square  law 
as  strictly  true.  For  only  a  small  range  in  velocity,  any  error  in  this  is 
inappreciable;  for  a  large  range,  it  may  be  necessary  to  take  different 
values  of  tHb  coefficient  at  different  velocities. 


52 


AIRPLANE    CHARACTERISTICS 


and  R  =  o.o6V2,  these  illustrating  the  variation  for  a  certain 
range  of  moderate  size  machines. 

Distribution  of  parasite  resistance. 

Parasite  resistance  is  roughly  distributed  about  as  follows : 
— body,  one-third;    wires  and  struts,  one-third;    tail  and 


600, 


40  60  80  100  1-20 

VELOCITY  -  -  MILES  PER  HOUR 

Fig.  33.     Variation  of  parasite  resistance  with  velocity;  the  three 
curves  show  R  =  0.02  V2,  R  -  0.04  V2  and  R  =  0.06  F2. 


landing  gear,  one-third  (about  one-sixth  for  tail  and  one-sixth 
for  landing  gear). 

Increase  of  parasite  resistance  due  to  propeller  slip  stream. 

Back  of  the  propeller  the  air  is  driven  backward  in  what 
is  called  the  slip  stream  or  propeller  race;  in  this  slip  stream 


RESISTANCE  53 

the  velocity  of  the  air  relative  to  the  airplane  is  increased, 
say,  20  or  2  5  per  cent.  V2  is  thus  increased  about  50  per  cent. 
The  parasite  resistance  of  the  tail  and  all  parts  of  the  structure 
in  the  slip  stream  is  accordingly  increased,  let  us  say,  50  per 
cent,  when  the  propeller  is  running.  Approximate  cal- 
culations may  be  made  on  this  basis.  Another  approxim- 
ate method  is  to  consider  that  the  increase  of  the  total 
parasite  resistance  due  to  the  propeller  slip  stream  is  10  per 
cent.  To  get  accurate  results,  careful  computation  would  be 
necessary. 

SOME  CONCLUSIONS 

Three  lines  for  improvement  are  suggested  by  the  forego- 
i  ng  discusions : — 

(1)  Reduce  parasite  resistance. 

(2 )  Reduce  weight. 

(3)  Improve  wing-section,  so  as  to  get  a  greater  L/D  ratio. 

Wing-resistance,  which  is  equal  to  weight  -i-  L/D,  is 
reduced  by  (2)  and  (3).  Most  important  are  (i)  and  (2),  as 
the  improvement  that  can  be  made  in  L  /D  ratio  is  probably 
rather  small. 

In  design  every  effort  should  be  made  to  reduce  weight 
and  to  cut  down  parasite  resistance. 

The  chief  weight  is  in  the  engine  and  the  reduction  of 
weight  is  largely  a  problem  for  the  engine  designer.  Re- 
duction in  parasite  resistance  is  to  be  looked  for  in  improved 
design  of  structure. 

Thrust  and  power  characteristics. 

The  reader  is  referred  to  Appendix  II  and  Appendix  III 
for  curves  showing  the  variation  of  thrust  and  power  required 
at  different  velocities. 


54  AIRPLANE  CHARACTERISTICS 

s 

For  horizontal  flight,  thrust  is  equal  to  the  total  resistance, 
i.  e.y  is  equal  to  the  sum  of  wing-resistance  and  parasite  re- 
sistance. 

Horse  power  is  equal  to  the  product  of  thrust  (in  pounds) 
and  velocity  (in  miles  per  hour)  divided  by  375. 

NOTE.  The  following  chapters  are  in  preparation  and 
logically  should  follow  Chapter  III.  Thrust.  Power. 
Climbing.  Gliding.  Altitude.  Single  and  Mutliple  Planes. 
Stability  in  General.  Longitudinal  Stability. 


CHAPTER   IV 

LATERAL   STABILITY 

Lateral  stability  of  an  airplane  is  stability  about  a  fore-and- 
aft  axis,  called  the  "rolling"  axis,  which  passes  through  the 
center  of  gravity  and  either  coincides  with  the  line  of  flight 
or  is  slightly  displaced  therefrom. 

Rolling  axis. 

The  rolling  axis  lies  in  the  plane  of  symmetry  of  the 
machine  and,  as  shown  in  Fig.  i,  it  may  be  either: 

A  neutral  axis,  when  it  coincides  exactly  with  the  line  of 

flight; 
A  raised  axis,  when  its  forward  end  is  raised  above  the  line 

of  flight  (the  common  case) ;  or, 

A  lowered  axis,  when  its  forward  end  is  lowered  below  the 
line  of  flight,  which  is  not  a  common  case. 


'FLIGHT  PATH 


Fig.  I .     Three  positions  of  rolling  axis. 

The  line  of  flight  is  always  understood  to  be  the  path  of  the 
center  of  gravity. 

Stability  requires  that  a  restoring  moment  be  set  up 
whenever  the  machine  is  displaced  from  its  normal  position. 
If  the  machine  is  rolled  over  to  one  side,  with  one  wing 
raised  and  the  other  lowered,  there  must  be  a  rolling  moment 
tending  to  roll  the  machine  back  until  the  two  wings  are 
again  on  the  same  level.  Although  for  steadiness  in  normal 

55 


56  AIRPLANE    CHARACTERISTICS 

flight  a  certain  positive  lateral  stability  is  desirable,  for  quick 
manceuvers  a  less  positive  or  even  an  indifferent  stability 
becomes  advantageous.  But  in  no  case  is  it  desirable  to  have 
a  negative  stability,  which  would  tend  to  overturn  the 
machine  when  once  displaced  from  its  normal  position. 

Neutral  axis. 

A  machine  with  a  neutral  axis  has,  from  symmetry,  a  neutral 
or  indifferent  stability,  inasmuch  as  the  angle  of  incidence  at 
which  the  air  strikes  the  various  surfaces  (including  keel  and 
other  surfaces  as  well  as  wings)  and  hence  also  the  pressure, 
remain  unchanged,  irrespective  of  any  displacement  of  the 
machine  about  its  rolling  axis.  The  displacement,  therefore, 
causes  neither  a  resorting  nor  an  upsetting  moment.  Such  a 
machine  needs  no  further  study.  By  "incidence"  is  always 
meant  the  angle  between  a  surface  and  the  stream  of  air  it 
encounters ;  in  case  of  a  curved  or  cambered  wing,  the  angle 
between  the  chord  and  the  air-stream. 

Inclined  axis. 

The  conditions  for  stability  in  a  machine  in  which  the 
rolling  axis  is  inclined  depend  upon  whether  the  axis  is  raised 
or  lowered  and  upon  the  disposition  of  keel  surfaces  and  upon 
the  shape  of  the  wings. 

Keel  surface  as  affecting  lateral  stability. 

An  important  element  in  lateral  stability  is  the  keel 
surface  which  includes  all  surfaces  that  can  be  seen  in  a 
"side  view"  of  the  machine,  that  is,  when  the  machine  is 
viewed  in  a  direction  perpendicular  to  the  plane  of  symmetry. 
The  keel  surface  of  body,  struts  and  other  structure  may  in 
itself  be  sufficient,  but  it  is  frequently  supplemented  by  a 
vertical  stabilizer  or  keel  so  as  to  give  a  keel  surface  of  desired 


LATERAL   STABILITY 


57 


size  and  location, — i.  e.,  either  a  high  keel  above  the  rolling 
axis  or  (rarely)  a  low  keel  below  the  rolling  axis,  as  may  be 
required  for  stability. 

Small  keel  surfaces  are  sometimes  placed  on  top  of  the 
wings,  when  this  position  suits  the  design  of  the  machine,  or 
between  the  wings  of  a  biplane.  The  keel  or  vertical  stabilizer 
is,  however,  more  commonly  in  the  rear  of  the  machine,  with 
the  rudder  hinged  to  its  back  edge,  as  shown  in  Fig.  12  of  the 
next  chapter. 

Raised  axis;  high  keel  gives  stability,  low  keel  gives  insta- 
bility.— Place  a  card  on  a  stick  or  wire,  so  as  to  make  a  flag- 
shaped  model  as  in  Fig.  2,  and  view  it  from  in  front  along  the 


Fig.  2.     Stable. 


Fig.  3.     Unstable. 


line  of  flight ;  let  the  stick  represent  the  rolling  axis  and  the 
surface  of  the  card  represent  the  keel  surface.  When  the 
model  is  thus  viewed  from  the  front  (from  the  left  in  the 
illustration),  it  will  be  seen  that  with  a  raised  axis  a  high  keel 
surface  is  stable,  for  when  displaced  by  rolling,  one  side  of  the 
keel  plane  is  exposed  to  the  wind  (in  the  model,  is  exposed  to 
view)  and  the  pressure  on  this  side  is  in  a  direction  to  restore 
the  plane  to  its  normal  position.  Likewise,  as  shown  in  Fig. 
3 ,  it  will  be  seen  that  with  a  raised  axis  a  low  keel  is  unstable. 

The  restoring  moment  is  seen  to  depend  upon  the  position 
of  the  keel  surface  with  respect  to  the  rolling  axis,  and  to  be 
independent  of  its  position  with  respect  to  the  center  of 
gravity, — that  is,  it  may  be  above  or  below  the  center  of 


58  AIRPLANE    CHARACTERISTICS 

gravity,  in  front  of  or  behind  it,  without  affecting  lateral 
stability.  (The  location  of  the  keel  surface  with  respect  to 
the  center  of  gravity  has,  however,  a  direct  effect,  on  direc- 
tional stability  discussed  later,  and  on  stability  in  gusts.) 

Lowered  axis;  low  keel  gives  stability,  high  keel  gives  insta- 
bility.— In  a  like  manner,  it  may  be  seen  that,  with  a  lowered 
rolling  axis  as  shown  in  Figs.  4  and  5,  a  low  keel  gives  sta- 
bility and  a  high  keel  gives  instability. 

As  the  center  of  pressure  on  the  keel  surface  is  never  very 
far  from  the  rolling  axis,  the  restoring  moment  is  correspond- 


Fig.  4.     Stable. 


ingly  small.  A  longer  lever  arm  and  hence  a  larger  moment 
would  be  obtained  if  the  keel  surface  were  located  well  out 
on  the  wings,  and  some  machines  have  keel  surfaces  so 
placed.  The  same  effect,  however,  is  practically  obtained  by 
turning  the  wings  up  so  as  to  form  a  dihedral  angle,  as 
discussed  below. 

Wing  shape,  as  affecting  lateral  stability. 

Lateral  stability  is  materially  affected  if  the  two  wings, 
instead  of  lying  in  a  straight  line,  when  viewed  from  in  front, 
are  turned  up  so  as  to  form  a  dihedral  angle  (or  V)  as  in  Figs. 
6  and  7,  or  are  made  to  retreat  as  in  Fig.  8,  or  are  given  a 
raked  end  as  shown  in  the  same  figure. 

The  dihedral  angle  (called  "lateral"  or  "transverse" 
dihedral  to  distinguish  it  from  the  "longitudinal"  dihedral 


LATERAL   STABILITY 


59 


angle  between  the  main  plane  and  tail)  may  be  caused  or 
noticably  increased  by  flexure  of  the  wings  in  flight.  The 
dihedral  angle  often  amounts  to  several  degrees  and  is  dis- 
tinctly noticeable,  but  it  may  be  so  small  (perhaps  one  degree 
or  less)  as  to  be  scarcely  noticeable  to  the  eye. 


DIHEDRAL  ANGLE o 
.V 


Figs.  6  and  7.     Dihedral  angle  for  monoplane 
and  biplane;  front  view. 


Model  to  show  effect  of  wing  shape. 

The  effect  of  wing  shape  upon  lateral  stability  depends 
upon  the  position  of  the  rolling  axis  and  this  is  best  seen  by 
inspection  of  a  model,  readily  made  from  a  small  rectangular 
board,  as  in  Fig.  9. 

Different  types  of  wings,  made  of  card  board  or  tin,  can 


„  SWEEP  BACK 
/   OR  RETREAT 


-  RAKED  END 


Fig.  8.     Showing  retreating  or  swept-back  wings;  showing 
also  raked  ends  to  wings.    Top  view. 

be  inserted  in  the  slits  i ,  2  or  3  to  obtain  different  angles  of 
incidence.  The  board  can  be  rotated  about  the  pegs  NN  for 
a  neutral  axis,  about  RR  for  a  raised  axis  and  about  LL  for  a 


60 


AIRPLANE    CHARACTERISTICS 


lowered  axis.     (Other  pegs  may  be  used  to  give  other  angles 
to  these  axes.) 

Lateral  Stability  as  affected  by  dihedral  angle. 

By  such  a  model  the  following  conclusions  can  be  readily 
verified. 

(i)  Dihedral  angle  (V)  and  raised  axis,  gives  stability, 
because,  when  the  machine  is  displaced  by  rolling: 

Raised  wing  has  a  smaller  angle  of  incidence  and  hence  less 
lift; 


N  — • 


—  N 


<  FLIGHT    PATH 

Fig.  9.  Model.  Wings  of  different  forms  are  inserted  in 
the  slits  i,  2  and  3  and  viewed  from  the  front  (from 
the  left  in  the  illustration)  the  line  sight  being  in  the 
direction  of  the  air  stream. 

Lowered  wing  has  a  greater  angle  of  incidence  and  hence 
more  lift. 

This  makes  a  restoring  moment  and  it  can  be  shown  that 
this  moment  is  greater  as  the  angle  of  incidence  at  which  the 
machine  is  flying  is  greater. 

Case  (i)  is  the  method  actually  employed  for  obtaining 
lateral  stability. 

(2)  Dihedral  angle  (V)  and  lowered  axis,  gives  instability, 
because,  when  machine  is  displaced  by  rolling: 


LATERAL   STABILITY  61 

Raised  wing  has  a  larger  angle  of  incidence  and  hence  more 

lift; 
Lowered  wing  has  smaller  angle  of  incidence  and  hence 

less  lift. 

This  makes  an  upsetting  moment,  which  can  be  shown  to 
be  greater  as  the  incidence*  is  greater. 
In  a  like  manner,  it  may  be  seen  that : 

(3)  Inverted  dihedral  (A)  and  raised  axis,  gives  instability. 

(4)  Inverted  dihedral  (A)  and  lowered  axis,  gives  stability. 
With  the  inverted  dihedral,  the  upsetting  or  restoring 

moment  is  less  as  incidence  is  greater.  The  inverted  dihedral 
is  practically  never  used,  although  machines  have  been  so 
made  and  flown.  It  may  be  noted  that  a  gull,  when  it  lowers 
its  head  as  it  flies  near  the  water  in  search  of  fish,  also  droops 
its  wings  so  as  to  make  an  inverted  dihedral;  in  this  way 
stability  is  secured  with  what  is  now  a  lowered  axis.  As  the 
head  is  raised  again  for  normal  flight  and  the  rolling  axis 
changes  from  a  lowered  axis  to  a  neutral  and  then  to  a  raised 
axis,  the  inverted  dihedral  (A)  may  be  seen  to  disappear  and 
an  upright  dihedral  (V)  to  take  its  place. 

A  dihedral  angle,  or  an  inverted  dihedral  angle,  makes  a 
tendency  for  a  machine  to  roll  when  struck  by  a  side  gust. 
Too  large  a  dihedral  angle  is,  accordingly,  undesirable;  but 
other  means  may  be  used  for  increasing  lateral  stability. 

Straight  wings. 

With  straight  wings,  that  is  when  there  is  no  dihedral,  the 
incidence  on  both  wings  is  always  the  same.  Irrespective  of 


"This  is  true  for  small  angles  of  incidence  only ,  *.  e.,  for  the  range 
employed  in  flight  in  which  the  lift  increases  with  incidence.  Were  the 
incidence  increased  beyond,  say,  14°  or  15°,  the  lift  and  the  restoring 
moment  would  decrease. 


62  AIRPLANE    CHARACTERISTICS 

whether  the  axis  is  raised  or  lowered,  there  is  no  difference 
in  the  incidence  of  the  two  wings  when  the  machine  rolls  and 
hence  no  restoring  or  upsetting  moment  due  to  this  cause. 

A  raised  axis,  however,  has  a  small  tendency  toward  sta- 
bility, because  when  the  machine  rolls  the  lowered  wing 
moves  forward  and  its  center  of  pressure  (which  is  always 
ahead  of  the  middle  of  a  plane)  now  moves  toward  the  wing- 
tip,  thus  increasing  the  lever  arm  of  the  lift  on  this  wing;  the 
raised  wing  on  the  other  hand  moves  backward  and  its  center 
of  pressure  moves  towards  the  body  of  the  machine,  thus 
decreasing  its  lever  arm.  •  There  is  thus  a  restoring  moment, 
obtained  with  straight  wings  and  a  raised  axis;  it  is 
much  less,  however,  than  the  restoring  moment  obtained  by 
using  a  dihedral  angle. 

In  a  similar  way,  a  lowered  axis  with  straight  wings  tends 
toward  instability. 

Retreating  wings  and  wings  with  raked  ends. 

Retreating  or  swept  back  wings,  with  a  raised  rolling  axis, 
give  lateral  stability,  for  (as  may  be  seen  by  inserting  such 
wings  in  the  model,  Fig.  9),  when  the  machine  rolls,  the 
descending  wing  moves  forward  and  enters  the  air  more 
squarely  so  as  to  attack  more  air  and  get  more  lift,  thus 
restoring  the  machine  to  its  position  of  equilibrium. 

In  a  like  manner  it  can  be  shown  by  the  model  that,  with 
a  raised  axis,  lateral  stability  is  increased  if  the  ends  of  the 
wings  are  raked,  i.  e.,  if  the  trailing  edge  is  longer  than  the 
entering  edge. 

With  a  lowered  axis,  retreating  wings  and  wings  with 
raked  ends  would  be  unstable. 

Retreating  wings  and  wings  with  raked  ends  are  thus  seen 
to  have  the  same  effect  as  a  dihedral  angle  upon  lateral 


LATERAL  STABILITY  63 

stability,  but  with  the  advantage  that  in  a  side  gust  they 
create  no  tendency  for  a  machine  to  roll.  It  will  be  shown 
later  that  all  three  devices — dihedral  angle,  retreating  wings 
and  raked  ends — give  directional  stability.  But  they  all 
have  the  disadvantage  of  reducing  the  so-called  lifting 
efficiency,  or  L/D  ratio,  i.  e.,  there  is  a  decrease  in  the  amount 
of  lift  for  a  given  wing-resistance. 

Effect  of  velocity  on  lateral  stability. 

All  stability,  depending  upon  the  pressure  of  relative  air 
upon  surfaces,  increases  as  the  velocity  increases. 

Control. 

Lateral  control  might  well  be  obtained  by  shifting  the 
center  of  gravity,  but  this  is  not  done.     It  has  been  obtained 


Fig.  10.     Aileron  independent 
of  main  wings. 

by  warping  (i.  e.,  distorting)  the  planes,  but  lateral  control 
is  now  generally  obtained  by  means  of  auxiliary  planes  or 
ailerons  which  may  be  independent  of  the  main  planes  (i.  e., 
between  the  two  planes  of  a  biplane  as  in  Fig.  10)  or  attached 
to  the  wings  as  wing  flaps,  as  in  Fig.  1 1 .  To  roll  the  machine 
the  pilot,  simultaneously,  turns  the  aileron  on  one  wing  down 
and  the  other  aileron  up,  thus  giving  more  lift  to  one  wing  so 
that  it  rises  and  less  left  to  the  other  so  that  it  descends. 
This  movement  of  the  ailerons  is  commonly  effected  by 
pushing  the  control  stick,  or  by  turning  the  control  wheel,  to 


64  AIRPLANE    CHARACTERISTICS 

left  or  to  right,  as  illustrated  in  Appendix  IV.  The  term 
"warping"  is  frequently  used  to  include  this  control  by 
ailerons. 

Banking  may  or  may  not  produce  turning. 

A  machine  is  said  to  be  banked  when  it  is  keeled  over  on 
a  turn,  as  a  bicycle  rider  leans  inward  on  a  curve. 

A  machine  is  banked  on  a  turn  by  elevating  one  wing  and 
depressing  the  other,  this  being  accomplished  by  manipulat- 


Fig.  ii.  Section  of  wing  with  wing-flap  or  aileron. 
In  (a)  the  wing-tip  and  aileron  normally  have 
positive  incidence;  in  (b)  they  are  up-turned  and 
have  negative  incidence. 

ing  the  ailerons  in  the  manner  described ;  but  this  manipula- 
tion of  the  ailerons  will  itself  tend  to  turn  the  machine  to  one 
side,  if  the  wing-resistance  is  thereby  increased  on  that  side 
and  decreased  on  the  other  side. 

If  the  raised  wing  has  its  resistance  increased  when  its 
aileron  is  turned  down,  and  the  lowered  wing  has  its  resistance 
decreased  when  its  aileron  is  turned  up  (as  will  occur  with 
many  wing  sections,  as  a  in  Fig.  n),  the  raised  wing  will  be 
retarded  and  the  machine  will  turn  toward  the  higher  (outer) 
wing.  Such  a  turn  is  not  desirable  but,  under  these  condi- 
tions, will  occur  unless  prevented  by  the  rudder. 

A  turn  toward  the  lower  (inner)  wing  is  more  desirable 
and  this  may  be  accomplished  by  having  the  wing  tips 
(including  ailerons)  somewhat  upturned  so  as  to  have  a 
negative  incidence  in  normal  flight;  see  b  in  Fig.  n.  The 


LATERAL   STABILITY  65 

resistance  of  the  raised  wing  is  then  decreased  when  its 
aileron  is  swung  down,  and  the  resistance  of  the  lowered  wing 
is  increased  as  its  aileron  is  swung  up,  so  that  the  lower  wing 
is  retarded  and  a  turn  is  made  toward  the  lower  (inner)  wing. 
Indeed  some  machines  are  made  so  as  to  depend  entirely 
upon  banking  as  a  means  for  turning,  no  rudder  being  pro- 
vided. (Conversely,  as  discussed  in  the  next  chapter,  turning 
produces  banking  and  in  some  machines  the  rudder  has  been 
the  only  means  for  banking,  no  ailerons  or  similar  devices 
being  provided.) 

Although  it  is  in  many  ways  desirable  to  have  a  machine 
thus  turn  in  automatically  when  it  is  banked,  some  prefer  to 
have  the  control  left  entirely  to  the  pilot,  the  machine  having 
no  tendency  to  turn  either  in  or  out.  This  condition  may  be 
approached  by  a  nicety  in  design  of  section  of  wing  and 
aileron.  The  negative  wing-tip  and  aileron, — although 
advantageous  for  the  reasons  just  described,  mean  a  sacrifice 
for  they  give  less  lift  and  greater  wing-resistance. 

There  is  room  for  difference  of  opinion  as  to  how  great  an 
extent  banking  and  turning  should  be  automatically  depend- 
ent upon  each  other  and  to  what  extent  their  control  should 
depend  upon  the  pilot. 

Propeller  Torque. 

In  a  machine  with  one  propeller,  as  the  propeller  rotates  in 
one  direction  there  is  a  tendency  (when  the  power  is  on)  for 
the  whole  machine  to  rotate  in  the  opposite  direction.  This 
may  be  easily  corrected  for  in  the  control  by  the  pilot,  or 
automatically  by  a  difference  in  the  lift  of  the  two  wings,  as 
described  below.  When  flying,  any  correction  is  made  by 
the  pilot  unconsciously.  When  starting,  however,  the  cor- 
rection may  be  noticeable,  for  the  amount  of  correction 


66  AIRPLANE   CHARACTERISTICS 

changes  as  the  engine  accelerates ;  furthermore  it  is  particu- 
larly important  while  near  the  ground  to  keep  both  wings 
even.  When  two  propellers  are  used,  rotating  in  opposite 
directions,  the  effects  of  propeller  torque  are  neutralized. 

Automatic  correction  for  propeller  torque. 

The  correction  for  the  torque  of  the  propeller  when  power 
is  on  is  often  made  automatically  by  a  lack  of  symmetry  in 
the  two  wings  so  that  one  wing  has  more  lift  than  the  other. 
This  is  sometimes  done  by  a  droop  and  rise  (a  droop  near  the 
end  of  one  wing  and  a  rise  near  the  end  of  the  other)  and 
sometimes  by  a  wash  out  on  one  wing  (a  progressive  decrease 
in  incidence  from  body  to  wing-tip)  and  a  wash  in  on  the 
other  wing  (a  progressive  increase  of  incidence  from  body  to 
wing-tip.) 

Any  such  lack  of  symmetry,  however,  gives  a  tendency  for 
the  machine  to  rotate  when  power  is  off.  In  horizontal 
flight  this  may  be  corrected  for  by  the  controls,  but  in  diving 
it  may  make  a  spin  that  can  not  be  controlled;  for  this 
reason  lack  of  symmetry  is  very  undesirable  and  should  be 
avoided. 


CHAPTER  V 

DIRECTIONAL  STABILITY 

When  an  airplane  swings  off  from  its  course,  to  left  or  right, 
it  is  said  to  yaw.  Directional  stability  is  the  stability  that 
keeps  a  machine  on  its  course,  that  is  it  restores  the  machine 
to  its  course  whenever  it  yaws.  The  vertical  or  yawing  axis 
passes  through  the  center  of  gravity  of  the  machine,  lies  in  the 
plane  of  symmetry  and  is  more  or  less  perpendicular  to  the 
flight  path. 

This  stability  is  similar  to  that  of  a  weathercock  and 
depends  upon  having  the  center  of  the  keel  surface  back  of  the 
yawing  axis,  thus  insuring  a  restoring  moment  whenever  the 
machine  departs  from  its  course.  It  is  to  be  remembered 
that  the  keel  surface  is  all  the  surface  seen  from  the  side, 
including  structure  as  well  as  auxiliary  keels  or  fins.  In 
some  machines  enough  directional  stability  is  obtained  by  the 
keel  surf  ace  of  the  body  itself,  but  this  is  usually  supplemented 
by  the  addition  of  a  small  keel  or  vertical  stabilizer  in  the 
rear.  If  the  keel  center  is  too  far  aft,  side  gusts  will  cause  the 
machine  to  yaw  too  much. 

A  machine  should  fly  straight  on  its  flight  path ;  but  it  will 
fail  to  do  so  and  will  proceed  crab-fashion  if  there  is  unequal 
resistance  on  the  two  sides .  This  might  be  caused  by  unequal 
incidence  of  the  two  wings,  distorted  surface  or  cambre,  lack 
of  symmetry  in  the  tail,  wrong  alignment  of  body  or  fin  or 
anything  that  might  act  as  a  rudder,  for  example  the  setting 
of  struts  or  stream-line  wires  not  in  the  line  of  flight, — points 
to  be  looked  at  in  "tuning  up"  a  machine. 

Dihedral  angle  and  retreating  wings. 

Although  the  keel  surface  is  the  chief  element  in  directional 

67 


68 


AIRPLANE    CHARACTERISTICS 


stability,  the  wings  may  contribute.  Directional  stability  is 
in  all  cases  aided  by  retreating  wings  and  by  wings  with  a 
transverse  dihedral  angle,  on  account  of  the  greater  resistance 
of  the  wing  which  advances  when  the  machine  swings  off  from 
its  course;  this  is  independent  of  the  location  of  the  rolling 
axis.  The  same  is  true  of  wings  with  raked  ends  (i.  e.  with 
trailing  edge  longer  than  entering  edge).  As  pointed  out  in 
the  preceding  chapter  (see  Figs.  6,  7  and  8)  these  forms  of 
wings  likewise  tend  toward  lateral  stability,  provided  there  is 
a  raised  rolling  axis. 


Fig.  12.     Vertical  stabilizer  (v)  and  rudder  (r). 

On  the  other  hand  an  inverted  dihedral  or  advancing  wing 
tips,  forms  of  wings  which  are  not  used,  would  in  all  cases 
tend  toward  directional  instability;  with  a  lowered  axis, 
these  forms  would,  however,  give  lateral  stability,  as  already 
explained. 

Turning. 

Turning  is  the  deflection  of  the  flight  path  to  left  or  right. 
Rotation  of  the  machine  about  its  vertical  axis,  although  it 
usually  accompanies  turning,  is  not  in  itself  sufficient. 
Although  turning  might  be  effected  by  other  means, — as  by 
shifting  the  center  of  gravity,  extending  a  panel  on  one  wing 


DIRECTIONAL   STABILITY  69 

to  increase  its  resistance,  etc. — it  is  usually  effected  by  a 
rudder  at  the  rear  of  the  machine.  This  is  often  hinged  on  a 
vertical  fin  or  stabilizer,  already  referred  to  in  connection 
with  lateral  stability,  which  forms  part  of  the  keel  surface; 
such  a  rudder  is  shown  in  Fig.  12.  A  balanced  rudder,  as  in 
Fig.  13,  reduces  the  force  necessary  for  control  and  for  this 
reason  is  commonly  used  on  large  machines.  The  rudder  is 
usually  operated  by  the  pilot's  feet,  as  illustrated  in 
Appendix  IV. 


Fig.  13.     Balanced  rudder  (r). 

Turning  by  rudder. 

A  rudder  alone  without  a  keel  would  be  ineffective,  for 
the  machine  when  rotated  by  the  rudder  would  tend  to 
skid  along  its  original  flight  path,  as  does  a  toboggan  on 
smooth  ice.  Turning  control  like  all  control  depends  also 
on  a  certain  speed,  as  in  watercraft  which  require  "steerage 
way"  in  order  to  answer  the  helm. 

The  relation  between  keel  and  rudder  in  turning  is  shown 
in  Fig.  14.  When  the  rudder  is  turned  to  one  side,  the  pres- 
sure on  the  rudder  causes  the  whole  machine  to  rotate  about 
its  vertical  axis  until  the  rudder  moment  (p  times  its  lever 
arm)  is  balanced  by  the  keel  moment  (the  keel  pressure  P 
times  its  lever  arm) ;  the  lever  arm  in  each  case  is  the  dis- 
tance measured  from  the  center  of  gravity  G,  to  the  force 
p  or  P,  measured  on  a  line  perpendicular  to  the  force. 


70  AIRPLANE    CHARACTERISTICS 

It  is  clear  that,  when  the  two  moments  are  equal,  the  force 
P,  with  the  shorter  lever  arm,  is  greater  than  p.  The  result- 
ant of  the  forces  P  and  p  is  a  force  R*  deflecting  the  machine 
from  its  original  flight  path. 

This  deflecting  force : 

Increases  as  P  increases  (increasing,  for  a  given  keel 
moment,  as  the  keel  surface  is  greater  and  its  distance 
from  G  is  less) ; 

Increases  as  p  decreases  (increasing,  for  a  given 
rudder  moment,  as  the  rudder  surface  is  smaller  and 
further  back.) 

A  rudder  is  most  effective,  therefore,  when  it  is  placed  far 
back,  and  the  keel  surface  is  placed  near  the  center  of  gravity. 

Secondary  effects. 

There  are  important  secondary  effects  on  turning,  the 
principal  ones  (see  Fig.  14)  being: 

(a)  Turning  causes  banking,  for  two  reasons:  (i)  The 
outer  wing  having  the  higher  velocity  and  greater  lift  tends 
to  rise  and  the  inner  wing  tends  to  descend  on  a  turn;  (2) 
The  pressure  on  the  keel  surface  on  a  turn  tends  to  keel  the 
machine  over  in  the  same  direction  as  in  (i),  provided  (as  is 
usually  the  case)  the  keel  center  is  above  the  rolling  axis. 
(In  some  machines,  as  mentioned  in  the  preceding  chapter, 


*Strictly  speaking,  R  is  not  the  resultant  of  P  and  p,  although  for  the 
present  purpose  it  may  be  so  called.  More  correctly,  P  and  p  may  each 
be  replaced  by  a  couple  and  by  a  force  acting  at  G,  these  two  forces 
being  shown  in  the  figure  by  light  dotted  lines.  The  two  couples  thus 
formed  are  equal  and  opposite  and  so  cancel  each  other.  This  leaves  the 
two  forces  acting  at  G  with  the  resultant  R. 

The  two  couples  thus  cancelled  do  not  affect  the  motion  of  the  air- 
plane as  a  whole;  they  do,  however,  enter  into  strength  computations. 


DIRECTIONAL   STABILITY 


71 


the  rudder  has  been  the  only  means  for  banking,  no  ailerons 
or  similar  devices  being  provided.) 

(b)  Turning  causes  increase  of  resistance  and  loss  of  speed 
due  to  the  fact  that  the  pressures  P  and  p  on  keel  and  rudder 
each  have  a  backward  component. 


COURSE: 

XAKCN 

\ 

\ 

ORIGINAL. 

COURSE: 

^-^ 

RVDDETR 

Fig.  14.     Action  of  keel  in  turning. 


(c)  Turning  causes  a  decrease  in  lift  and  a  tendency  to 
descend,  i.  e.,  a  tendency  to  stall,  for  two  reasons:  (i)  On 
account  of  loss  of  speed  described  in  b,  the  pressure  on  the 
wings,  and  hence  the  lift,  is  decreased;  (2)  On  account  of 
banking  described  in  a,  the  vertical  component  of  the  lift  is 
decreased,  see  Fig.  1 5 ;  this  component  becoming  zero  when  a 
machine  is  banked  ninety  degrees. 


72 


AIRPLANE    CHARACTERISTICS 


(d)  Machine  may  nose  up  on  a  turn  and  thus  have  a  further 
tendency  to  stall,  if  the  pressures  P  and  p  on  keel  and  rudder 
are  higher  than  G,  on  account  of  the  backward  component  of 
these  pressures.  Stalling  may  end  in  a  tail  slide. 

The  tendency  to  stall  on  a  turn  may  be  overcome,  if  neces- 
sary, by  maintaining  speed  either  by  putting  on  more  power 
or  by  nosing  down  a  little  by  means  of  the  elevator.  Loss 
of  speed  is  to  be  avoided.  Obviously,  to  attempt  to  climb  on 
a  turn  is  dangerous. 


Fig.  15.     Horizontal  and  vertical  components 

lift  when  banking  note  that  lift  is 

not  vertical. 


Side  slipping  and  skidding. 

If  a  machine  is  banked  too  much  for  a  particular  turn,  it 
will  slip  in  and  down,  on  account  of  the  horizontal  component* 
there  is  to  the  lift  (see  Fig.  15)  and  the  decrease  in  the  vertical 
component.  This  may  result  in  a  nose  dive. 

If  a  machine  is  not  banked  enough,  it  will  skid  out  and  (in 
some  cases,  due  to  the  inertia  of  the  machine)  up,  this  being 
likely  to  happen  on  sharp  turns  and  at  high  speeds.  This 
may  end  in  a  stall,  as  the  relative  wind  strikes  the  machine 


*It  is  to  be  kept  in  mind  that  lift,  as  the  term  is  used,  lies  in  the  plane 
of  symmetry  of  a  machine  and  becomes  inclined  when  a  machine  rolls. 


DIRECTIONAL  STABILITY  73 

less  from  the  front  and  more  from  the  side  and  so  gives  less 
support  to  the  machine  on  account  of  its  decreased  forward 
velocity. 

Banking  on  a  turn. 

With  the  proper  banking,  the  centripetal  force  towards  the 
center  of  the  turn  due  to  the  banking  must  just  equal  the 
centrifugal  force  away  from  the  center.  There  being  no 
skidding  or  side  slipping,  the  pilot  will  feel  no  side  wind  on 
either  cheek.  He  will  feel  a  pressure  holding  him  to  his  seat 
with  no  pressure  to  left  or  right.  Strings  tied  to  guy- wires, 
blow  straight  back  and  not  at  an  angle.  If  rolling  is  indi- 
cated by  an  inclinometer  like  a  level  (arched  upward),  placed 
across  the  machine,  the  bubble  remains  central.  In  skidding 
or  side  slipping,  the  machine  leaves  the  bubble  behind;  the 
pilot  ought  to  keep  in  mind  that  the  control  should  follow 
the  bubble.  It  is  a  good  plan  to  start  banking  just  before 
beginning  a  turn. 

The  pilot  instinctively  gets  the  proper  "feel"  of  a  turn,  as 
does  the  rider  of  a  bicycle,  without  a  study  of  moments  and 
couples.  The  bicycle  rider,  however,  usually  learns  by  taking 
a  few  spills, — but  this  the  air  pilot  can  not  afford  to  do. 

Turning  by  banking. 

When  the  wings  are  inclined,  whatever  the  cause,  the  lift 
on  the  wings  has  not  only  a  vertical  component  but  also  a 
horizontal  sideways  component,  as  shown  in  Fig.  15,  which 
tends  to  move  the  machine  horizontally  toward  the  side  of 
the  machine  that  is  down.  The  flight  path  is  thus  deflected. 
This  becomes  more  pronounced  in  machines  with  large  keel 
surface.  By  placing  large  keel  surfaces,  both  forward  and 
aft,  certain  machines  are  turned  entirely  by  banking  and  are 
provided  with  no  rudder. 


74  AIRPLANE   CHARACTERISTICS 

Gryoscopic  action. 

The  propeller  and  revolving  parts  of  the  engine  form  a 
gyroscope,  so  that  a  sudden  turn  of  the  machine  sideways 
will  cause  it  to  pitch  or  rear.  Similarly  any  sudden  pitching 
or  rearing  will  cause  the  machine  to  turn  to  one  side;  for, 
when  a  sudden  force  is  applied  perpendicular  to  the  axis  of  a 
gyroscope,  the  axis  swings  sideways  at  right  angles  to  that 
force.  The  direction  of  this  effect  will  depend  upon  the  direc- 
tion of  rotation  of  the  revolving  parts,  and  so  may  be  opposite 
in  different  machines.  This  effect  will  be  but  small  when 
controls  are  not  jerked  suddenly;  indeed  they  should  not  be 
operated  suddenly  on  account  of  the  severe  stresses  produced. 


APPENDICES 

APPENDIX     I.  Glossary. 

APPENDIX    II.  Thrust  Characteristics. 

APPENDIX  III.  Power  Characteristics. 

APPENDIX  IV.  Control  and  Other  Diagrams. 


75 


APPENDIX  I 

GLOSSARY* 

AEROFOIL:  A  winglike  structure,  flat  or  curved,  designed 
to  obtain  reaction  upon  its  surface  from  the  air  through 
which  it  moves. 

AEROPLANE  :    See  Airplane. 

AILERON:  A  movable  auxiliary  surface  used  to  produce  a 
rolling  moment  about  the  fore-and-aft  axis. 

AIRCRAFT:  Any  form  of  craft  designed  for  the  navigation 
of  the  air — airplanes,  balloons,  dirigibles,  helicopters,  kites, 
kite  balloons,  ornithopters,  gliders,  etc. 

AIRPLANE:  A  form  of  aircraft  heavier  than  air  which  has 
wing  surfaces  for  support  in  the  air,  with  stabilizing  sur- 
faces, rudders  for  steering,  and  power  plant  for  propulsion 
through  the  air.  This  term  is  commonly  used  in  a  more 
restricted  sense  to  refer  to  air-planes  fitted  with  landing 
gear  suited  to  operation  from  the  land.  If  the  landing 
gear  is  suited  to  operation  from  the  water,  the  term  "sea- 
plane" is  used.  (See  definition.) 

Pusher. — A  type  of  airplane  with  the  propeller  in  the 

rear  of  the  engine. 
Tractor. — A  type  of  airplane  with  the  propeller  in  front 

of  the  engine. 

AIR-SPEED  METER:  An  instrument  designed  to  measure  the 
speed  of  an  aircraft  with  reference  to  the  air. 

ALTIMETER  :  An  aneroid  mounted  on  an  aircraft  to  indicate 
continuously  its  height  above  the  surface  of  the  earth. 

ANEMOMETER:  Any  instrument  for  measuring  the  velocity 
of  the  wind. 


*From  Report  No.  15,  on  "Nomenclature  for  Aeronautics,"  by  the 
National  Advisory  Committee  for  Aeronautics. 

77 


78  AIRPLANE   CHARACTERISTICS 

ANGLE  : 

Of  attack  or  of  incidence  of  an  aerofoil. — The  acute  angle 
between  the  direction  of  the  relative  wind  and  the 
chord  of  an  aerofoil;  i.  e.,  the  angle  between  the  chord 
of  an  aerofoil  and  its  motion  relative  to  the  air. 
(This  definition  may  be  extended  to  any  body  having 
an  axis.) 

Critical. — The  angle  of  attack  at  which  the  lift-curve  has 
its  first  maximum;  sometimes  referred  to  as  the 
"burble  point."  (If  the  "lift  curve"  has  more  than 
one  maximum,  this  refers  to  the  first  one.) 

Gliding. — The  angle  the  flight  path  makes  with  the  hori- 
zontal when  flying  in  still  air  under  the  influence  of 
gravity  alone,  i.  e.,  without  power  from  the  engine. 

APPENDIX  :  The  hose  at  the  bottom  of  a  balloon  used  for 
inflation.  In  the  case  of  a  spherical  balloon  it  also  serves 
for  equalization  of  pressure. 

ASPECT  RATIO  :    The  ratio  of  span  to  chord  of  an  aerofoil. 

AVIATOR:  The  operator  or  pilot  of  heavier-than-air  craft. 
This  term  is  applied  regardless  of  the  sex  of  the  operator. 

AXES  OF  AN  AIRCRAFT:  Three  fixed  lines  of  reference; 
usually  centroidal  and  mutually  rectangular. 

The  principal  longitudinal  axis  in  the  plane  of  symmetry, 
usually  parallel  to  the  axis  of  the  propeller,  is  called  the  fore 
and  aft  axis  (or  longitudinal  axis) ;  the  axis  perpendicular 
to  this  in  the  plane  of  symmetry  is  called  the  vertical  axis ; 
and  the  third  axis,  perpendicular  to  the  other  two,  is  called 
the  transverse  axis  (or  lateral  axis).  In  mathematical 
discussions  the  first  of  these  axes,  drawn  from  front  to  rear, 
is  called  the  X  axis;  the  second,  drawn  upward,  the  Z  axis; 
and  the  third,  forming  a  "left-handed"  system,  the  Y  axis. 

BALANCING  FLAPS  :    See  Aileron. 

BALLONET  :  A  small  balloon  within  the  interior  of  a  balloon 
or  dirigible  for  the  purpose  of  controlling  the  ascent  or 
descent,  and  for  maintaining  pressure  on  the  outer  envelope 
so  as  to  prevent  deformation.  The  ballonet  is  kept  inflated 


GLOSSARY  79 

with  air  at  the  required  pressure,  under  the  control  of  a 
blower  and  valves. 

BALLOON:  A  form  of  aircraft  comprising  a  gas  bag  and  a 
basket.  The  support  in  the  air  results  from  the  buoyancy 
of  the  air  displaced  by  the  gas  bag,  the  form  of  which  is 
maintained  by  the  pressure  of  a  contained  gas  lighter  than 
air. 

Barrage. — A  small  spherical  captive  balloon,  raised  as  a 

protection  against  attacks  by  airplanes. 
Captice. — A  balloon  restrained  from  free  flight  by  means 

of  a  cable  attaching  it  to  the  earth. 
Kite. — An  elongated  form  of  captive  balloon,  fitted  with 
tail  appendages  to  keep  it  headed  into  the  wind,  and 
deriving  increased  lift  due  to  its  axis  being  inclined  to 
the  wind. 
Pilot. — A  small  spherical  balloon  sent  up  to  show  the 

direction  of  the  wind. 

Sounding. — A  small  spherical  balloon  sent  aloft,  without 
passengers,  but  with  registering  meteorological  instru- 
ments. 

BALLOON  BED  :  A  mooring  place  on  the  ground  for  a  captive 
balloon. 

BALLOON  CLOTH:  The  cloth,  usually  cotton,  of  which 
balloon  fabrics  are  made. 

BALLOON  FABRIC  :  The  finished  material,  usually  rubberized, 
of  which  balloon  envelopes  are  made. 

BANK  :  To  incline  an  airplane  laterally — i.  e.,  to  roll  it  about 
the  fore  and  aft  axis.  Right  bank  is  to  incline  the  airplane 
with  the  right  wing  down  Also  used  as  a  noun  to  describe 
the  position  of  an  airplane  when  its  lateral  axis  is  inclined 
to  the  horizontal. 

BAROGRAPH:  An  instrument  used  to  record  variations  in 
barometric  pressure.  In  aeronautics  the  charts  on  which 
the  records  are  made  indicate  altitudes  directly  instead  of 
barometric  pressures. 


80  AIRPLANE    CHARACTERISTICS 

BASKET:  The  car  suspended  beneath  a  balloon,  for  passen- 
gers, ballast,  etc. 

BIPLANE:  A  form  of  airplane  in  which  the  main  supporting 
surface  is  divided  into  two  parts,  one  above  the  other. 

BODY  OF  AN  AIRPLANE:  The  structure  which  contains  the 
power  plant,  fuel,  passengers,  etc. 

BONNET  :  The  appliance,  having  the  form  of  a  parasol,  which 
protects  the  valve  of  a  spherical  balloon  against  rain. 

BRIDLE:  The  system  of  attachment  of  cable  to  a  balloon, 
including  lines  to  the  suspension  band. 

BULLSEYES:  Small  rings  of  wood,  metal,  etc.,  forming  part 
of  balloon  rigging,  used  for  connection  or  adjustment  of 
ropes. 

BURBLE  POINT  :     See  Angle,  critical. 

CABANE  :  A  pyramidal  framework  upon  the  wing  of  an  air- 
plane, to  which  stays,  etc.,  are  secured. 

CAMBER:  The  convexity  or  rise  of  the  curve  of  an  aerofoil 
from  its  chord,  usually  expressed  as  the  ratio  of  the  maxi- 
mum departure  of  the  curve  from  the  chord  to  the  length 
of  the  chord.  "Top  camber' '  refers  to  the  top  surface  of  an 
aerofoil,  and  "bottom  camber"  to  the  bottom  surface; 
"mean  camber"  is  the  mean  of  these  two. 

CAPACITY  :    See  Load. 

The  cubic  contents  of  a  balloon. 

CENTER  :  Of  pressure  of  an  aerofoil. — The  point  in  the  plane 
of  the  chords  of  an  aerofoil,  prolonged  if  necessary,  through 
which  at  any  given  attitude  the  line  of  action  of  the 
resultant  air  force  passes.  (This  definition  may  be 
extended  to  any  body.) 

CHORD : 

Of  an  aerofoil  section. — A  right  line  tangent  at  the  front 
and  rear  to  the  under  curve  of  an  aerofoil  section. 

Length. — The  length  of  the  chord  is  the  length  of  the  pro- 
jection of  the  aerofoil  section  on  the  chord. 


GLOSSARY  81 

CLINOMETER:     See  Inclinometer. 

CONCENTRATION  RING:  A  hoop  to  which  are  attached  the 
ropes  suspending  the  basket. 

CONTROLS  :  A  general  term  applying  to  the  means  provided 
for  operating  the  devices  used  to  control  speed,  direction  of 
flight,  and  attitude  of  an  aircraft. 

CONTROL  COLUMN:  The  vertical  lever  by  means  of  which 
certain  of  the  principal  controls  are  operated,  usually 
those  for  pitching  and  rolling. 

CROW'S  FOOT:  A  system  of  diverging  short  ropes  for  dis- 
tributing the  pull  of  a  single  rope. 

DECALAGE  :  The  angle  between  the  chords  of  the  principal 
and  the  tail  planes  of  a  monopolane.  The  same  term  may 
be  applied  to  the  corresponding  angle  between  the  direction 
of  the  chord  or  chords  of  a  biplane  and  the  direction  of  a 
tail  plane.  (This  angle  is  also  sometimes  known  as  the 
longitudinal  V  of  the  two  planes.) 

DIHEDRAL  IN  AN  AIRPLANE  :  The  angle  included  at  the  inter- 
section of  the  imaginary  surfaces  containing  the  chords  of 
the  right  and  left  wings  (continued  to  the  plane  of  symme- 
try if  necessary).  This  angle  is  measured  in  a  plane  per- 
pendicular to  that  intersection.  The  measure  of  the 
dihedral  is  taken  as  90°  minus  one-half  of  this  angle  as 
defined. 

The  dihedral  of  the  upper  wing  may  and  frequently  does 
differ  from  that  of  the  lower  wing  in  a  biplane. 
DIRIGIBLE  :    A  form  of  balloon,  the  outer  envelope  of  which 
is  of  elongated  form,  provided  with  a  propelling  system, 
car,  rudders,  and  stabilizing  surfaces. 

Nonrigid. — A  dirigible  whose  form  is  maintained  by  the 
pressure  of  the  contained  gas  assisted  by  the  car- 
suspension  system. 
Rigid. — A  dirigible  whose  form  is  maintained  by  a  rigid 

structure  contained  within  the  evnelope. 
Semirigid. — A  dirigible  whose  form  is  maintained  by 
means  of  a  rigid  keel  and  by  gas  pressure. 


82  AIRPLANE   CHARACTERISTICS 

DIVING  RUDDER:    See  Elevator. 

DOPE  :  A  general  term  applied  to  the  material  used  in  treat- 
ing the  cloth  surface  of  airplane  members  and  balloons  to 
increase  strength,  produce  tautness,  and  act  as  a  filler  to 
maintain  air-tightness;  it  usually  has  a  cellulose  base. 

DRAG  :  The  component  parallel  to  the  relative  wind  of  the 
total  force  on  an  aircraft  due  to  the  air  through  which  it 
moves. 

That  part  of  the  drag  due  to  the  wings  is  called  "wing 
resistance"  (formerly  called  "drift");  that  due  to  the  rest 
of  the  airplane  is  called  "parasite  resistance"  (formerly 
called  "head  resistance"). 

DRIFT:  See  Drag.  Also  used  as  synonymous  with  "lee- 
way," q.  v. 

DRIFT  METER:  An  instrument  for  the  measurement  of  the 
angular  deviation  of  an  aircraft  from  a  set  course,  due  to 
cross  winds. 

DRIP  CLOTH:  A  Curtain  around  the  equator  of  a  balloon, 
which  prevents  rain  from  dripping  into  the  basket. 

ELEVATOR  :  A  hinged  surface  for  controlling  the  longitudinal 
attitude  of  an  aircraft;  i.  e.,  its  rotation  about  the  trans- 
verse axis. 

EMPANNAGE  :    See  Tail. 

ENTERING  EDGE:  The  foremost  edge  of  an  aerofoil  or  pro- 
peller blade. 

ENVELOPE:  The  portion  of  the  balloon  or  dirigible  which 
contains  the  gas. 

EQUATOR:  The  largest  horizontal  circle  of  a  spherical 
balloon. 

FINS  :  Small  fixed  aerofoils  attached  to  different  parts  of  air- 
craft, in  order  to  promote  stability;  for  example,  tail  fins, 
skid  fins,  etc.  Fins  are  often  adjustable.  They  may  be 
either  horizontal  or  vertical. 

FLIGHT  PATH  :  The  path  of  the  center  of  gravity  of  an  air- 
craft with  reference  to  the  earth. 


GLOSSARY  83 

FLOAT  :  That  portion  of  the  landing  gear  of  an  aircraft  which 
provides  buoyancy  when  it  is  resting  on  the  surface  of  the 
water. 

FUSELAGE  :    See  Body. 

GAP  :  The  shortest  distance  between  the  planes  of  the  chords 
of  the  upper  and  lower  wings  of  a  biplane. 

GAS  BAG  :     See  Envelope. 

GLIDE  :     To  fly  without  engine  power. 

GLIDER  :  A  form  of  aircraft  similar  to  an  airplane,  but  with- 
out any  power  plant. 

When  utilized  in  variable  winds  it  makes  use  of  the  soar- 
ing principles  of  flight  and  is  sometimes  called  a  soaring 
machine. 

GORE  :   One  of  the  segments  of  fabric  composing  the  envelope. 

GROUND  CLOTH  :  Canvas  placed  on  the  ground  to  protect  a 
balloon. 

GUIDE  ROPE  :  The  long  trailing  rope  attached  to  a  spherical 
balloon  or  dirigible,  to  serve  as  a  brake  and  as  a  variable 
ballast. 

GUY:  A  rope,  chain,  wire,  or  rod  attached  to  an  object  to 
guide  or  steady  it,  such  as  guys  to  wing,  tail,  or  landing  gear. 

HANGAR  :    A  shed  for  housing  balloons  or  airplanes. 

HELICOPTER:  A  form  of  aircraft  whose  support  in  the  air  is 
derived  from  the  vertical  thrust  of  propellers. 

HORN:  A  short  arm  fastened  to  a  movable  part  of  an  air- 
plane, serving  as  a  lever-arm,  e.  g.,  aileron-horn,  rudder- 
horn,  elevator-horn. 

INCLINOMETER:  An  instrument  for  measuring  the  angle 
made  by  any  axis  of  an  aircraft  with  the  horizontal,  often 
called  a  clinometer. 

INSPECTION  WINDOW:  A  small  transparent  window  in  the 
envelope  of  a  balloon  or  in  the  wing  of  an  airplane  to  allow 
inspection  of  the  interior. 


84  AIRPLANE   CHARACTERISTICS 

KITE:  A  form  of  aircraft  without  other  propelling  means 
than  the  towline  pull,  whose  support  is  derived  from  the 
force  of  the  wind  moving  past  its  surface. 

LANDING  GEAR  :  The  understructure  of  an  aircraft  designed 
to  carry  the  load  when  resting  on  or  running  on  the  surface 
of  the  land  or  water. 

LEADING  EDGE:     See  Entering  edge. 

LEEWAY  :  The  angular  deviation  from  a  set  course  over  the 
earth,  due  to  cross  currents  of  wind,  also  called  drift; 
hence,  "drift  meter." 

LIFT:  The  component  perpendicular  to  the  relative  wind, 
in  a  vertical  plane,  of  the  force  on  an  aerofoil  due  to  the  air 
pressure  caused  by  motion  through  the  air. 

LIFT  BRACING  :    See  Stay. 

LOAD: 

Dead. — The  structure,  power  plant,  and  essential  acces- 
sories of  an  aircraft. 

Full. — The  maximum  weight  which  an  aircraft  can  sup- 
port in  flight;  the  "gross  weight." 

Useful. — The  excess  of  the  full  load  over  the  dead-weight 
of  the  aircraft  itself,  i.  e.,  over  the  weight  of  its  struc- 
ture, power  plant,  and  essential  accessories.  (These 
last  must  be  specified.) 

LOADING  :    See  Wing,  loading. 

LOBES  :     Bags  at  the  stern  of  an  elongated  balloon  designed 
to  give  it  directional  stability. 

LONGERON  :    See  Longitudinal. 

LONGITUDINAL  :  A  fore-and-aft  member  of  the  framing  of  an 
air-plane  body,  or  of  the  floats,  usually  continuous  across  a 
number  of  points  of  support. 

MONOPLANE  :  A  form  of  airplane  whose  main  supporting  sur- 
face is  a  single  wing,  extending  equally  on  each  side  of  the  body . 

MOORING  BAND  :  The  band  of  tape  over  the  top  of  a  balloon 
to  which  are  attached  the  mooring  ropes. 


GLOSSARY  85 

NACELLE:     See  Body.     Limited  to  pushers. 

NET:  A  rigging  made  of  ropes  and  twine  on  spherical  bal- 
loons, which  supports  the  entire  load  carried. 

ORNITHOPTER:  A  form  of  aircraft  deriving  its  support  and 
propelling  force  from  flapping  wings. 

PANEL:  The  unit  piece  of  fabric  of  which  the  enevelope  is 
made. 

PARACHUTE  :  An  apparatus,  made  like  an  umbrella,  used  to 
retard  the  descent  of  a  falling  body. 

PATCH  SYSTEM  :  A  system  of  construction  in  which  patches 
(or  adhesive  flaps)  are  used  in  place  of  the  suspension  band. 

PERMEABILITY.  The  measure  of  the  loss  of  gas  by  diffusion 
through  the  intact  balloon  fabric. 

PITOT  TUBE  :  A  tube  with  an  end  open  square  to  the  fluid 
stream,  used  as  a  detector  of  an  impact  pressure.  It  is 
usually  associated  with  a  coaxial  tube  surrounding  it, 
having  perforations  normal  to  the  axis  for  indicating  static 
pressure ;  or  there  is  such  a  tube  placed  near  it  and  parallel 
to  it,  with  a  closed  conical  end  and  having  perforations  in 
its  side.  The  velocity  of  the  fluid  can  be  determined  from 
the  difference  between  the  impact  pressure  and  the  static 
pressure,  as  read  by  a  suitable  gauge.  This  instrument  is 
often  used  to  determine  the  velocity  of  an  aircraft  through 
the  air. 

PONTOONS  :    See  Float. 

PUSHER  :     See  Airplane. 

PYLON  :    A  mast  or  pillar  serving  as  a  marker  of  a  course. 

RACE  OF  A  PROPELLER:     See  Slip  stream. 

RELATIVE  WIND  :  The  motion  of  the  air  with  reference  to  a 
moving  body.  Its  direction  and  velocity,  therefore,  are 
found  by  adding  two  vectors,  one  being  the  velocity  of  the 
air  with  reference  to  the  earth,  the  other  being  equal  and 
opposite  to  the  velocity  of  the  body  with  reference  to  the 
earth. 


86  AIRPLANE    CHARACTERISTICS 

RIP  CORD  :  The  rope  running  from  the  rip  panel  of  a  balloon 
to  the  basket,  the  pulling  of  which  causes  immediate 
deflation. 

RIP  PANEL  :  A  strip  in  the  upper  part  of  a  balloon  which  is 
torn  off  when  immediate  deflation  is  desired. 

RUDDER  :  A  hinged  or  pivoted  surface,  usually  more  or  less 
flat  or  stream  lined,  used  for  the  purpose  of  controlling  the 
attitude  of  an  aircraft  about  its  "vertical"  axis,  i.  e.,  for 
controlling  its  lateral  movement. 

Rudder  bar. — The  foot  bar  by  means  of  which  the  rudder 
is  operated. 

SEAPLANE  :  A  particular  form  of  airplane  in  which  the  land- 
ing gear  is  suited  to  operation  from  the  water. 

SERPENT  :    A  short,  heavy  guide  rope. 

SIDE  SLIPPING  :  Sliding  downward  and  inward  when  making 
a  turn;  due  to  excessive  banking.  It  is  the  opposite  of 
skidding. 

SKIDDING:  Sliding  sideways  away  from  the  center  of  the 
turn  in  flight.  It  is  usually  caused  by  insufficient  banking 
in  a  turn,  and  is  the  opposite  of  side  slipping. 

SKIDS  :  Long  wooden  or  metal  runners  designed  to  prevent 
nosing  of  a  land  machine  when  landing  or  to  prevent  drop- 
ping into  holes  or  ditches  in  rough  ground.  Generally 
designed  to  function  should  the  landing  gear  collapse  or 
fail  to  act. 

SLIP  STREAM  OR  PROPELLER  RACE  i  The  stream  of  air  driven 
aft  by  the  propeller  and  with  a  velocity  relative  to  the  air- 
plane greater  than  that  of  the  surrounding  body  of  still  air. 

SOARING  MACHINE  :    See  Glider. 

SPAN  OR  SPREAD  :  The  maximum  distance  laterally  from  tip 
to  tip  of  an  airplane  wing,  or  the  lateral  dimension  of  an 
aerofoil. 


GLOSSARY  87 

STABILITY  :  A  quality  in  virtue  of  which  an  airplane  in  flight 
tends  to  return  to  its  previous  attitude  after  a  slight  dis- 
turbance. 

Directional. — Stability  with  reference  to  the  vertical  axis. 

Dynamical. — The  quality  of  an  aircraft  in  flight  which 
causes  it  to  return  to  a  condition  of  equilibrium  after 
its  attitude  has  been  changed  by  meeting  some  dis- 
turbance, e.  g.,  a  gust.  This  return  to  equilibrium  is 
due  to  two  factors;  first,  the  inherent  righting 
moments  of  the  structure;  second,  the  damping  of 
the  oscillations  by  the  tail,  etc. 

Inherent. — Stability  of  an  aircraft  due  to  the  disposition 
and  arrangement  of  its  fixed  parts — i.  e.,  that  property 
which  causes  it  to  return  to  its  normal  attitude  of 
flight  without  the  use  of  the  controls. 

Lateral. — Stability  with  reference  to  the  longitudinal  (or 
fore  and  aft)  axis. 

Longitudinal. — Stability  with  reference  to  the  lateral 
axis. 

Statical. — In  wind  tunnel  experiments  it  is  found  that 
there  is  a  definite  angle  of  attack  such  that  for  a  greater 
angle  or  a  less  one  the  righting  moments  are  in  such  a 
sense  as  to  tend  to  make  the  attitude  return  to  this 
angle.  This  holds  true  for  a  certain  range  of  angles  on 
each  side  of  this  definite  angle;  and  the  machine  is 
said  to  possess  "statical  stability"  through  this  range. 

STABILIZER:  Any  device  designed  to  steady  the  motion  of 
aircraft. 

STAGGER:  The  amount  of  advance  of  the  entering  edge  of 
the  upper  wing  of  a  biplane  over  that  of  the  lower,  expressed 
as  percentage  of  gap;  it  is  considered  positive  when  the 
upper  surface  is  forward. 

STALLING:  A  term  describing  the  condition  of  an  airplane 
which  from  any  cause  has  lost  the  relative  speed  necessary 
for  control. 


88  AIRPLANE    CHARACTERISTICS 

STATOSCOPE:  An  instrument  to  detect  the  existence  of  a 
small  rate  of  ascent  or  descent,  principally  used  in  balloon- 
ing. 

STAY  :  A  wire,  rope,  or  the  like  used  as  a  tie  piece  to  hold 
parts  together,  or  to  contribute  stiffness;  for  example,  the 
stays  of  the  wing  and  body  trussing. 

STEP  :    A  break  in  the  form  of  the  bottom  of  a  float. 

STREAM-LINE  FLOW  :  A  term  in  hydromechanics  to  describe 
the  condition  of  continuous  flow  of  a  fluid,  as  distinguished 
from  eddying  flow. 

STREAM-LINE  SHAPE:    A  shape  intended  to  avoid  eddying 
and  to  preserve  stream-line  flow. 

STRUT:  A  compression  member  of  a  truss  frame;  for 
instance,  the  vertical  members  of  the  wing  truss  of  a 
biplane. 

SUSPENSION  BAND  :  The  band  around  a  balloon  to  which  are 
attached  the  basket  and  the  main  bridle  suspensions. 

SUSPENSION  BAR:  The  bar  used  for  the  concentration  of 
basket  suspension  ropes  in  captive  balloons. 

SWEEP  BACK  :  The  horizontal  angle  between  the  lateral  axis 
of  an  airplane  and  the  entering  edge  of  the  main  planes. 

TAIL  :  The  rear  portion  of  an  aircraft,  to  which  are  usually 
attached  rudders,  elevators,  stabilizers,  and  fins. 

TAIL  CUPS:  The  steadying  device  attached  at  the  rear  of 
certain  types  of  elongated  captive  balloons. 

THIMBLE:  An  elongated  metal  eye  spliced  in  the  end  of  a 
rope  or  cable. 

TRACTOR  :     See  Airplane. 

TRAILING  EDGE:  The  rearmost  edge  of  an  aerofoil  or  pro- 
peller blade. 

TRIPLANE  :  A  form  of  airplane  whose  main  supporting  sur- 
face is  divided  into  three  parts,  superimposed. 


GLOSSARY  89 

TRUSS:  The  framing  by  which  the  wing  loads  are  trans- 
mitted to  the  body ;  comprises  struts,  stays,  and  spars. 

UNDERCARRIAGE  :    See  Landing  gear. 

WARP  :    To  change  the  form  of  the  wing  by  twisting  it. 

WASH  OUT  :  A  permanent  warp  of  an  aerofoil  such  that  the 
angle  of  attack  decreases  toward  the  wing  tips. 

WEIGHT:     Gross.     See  Load,  full. 

WINGS  :     The  main  supporting  surfaces  of  an  airplane. 

WING  FLAP:    See  Aileron. 

WING  LOADING:  The  weight  carried  per  unit  area  of  sup- 
porting surface. 

WING  MAST  :  The  mast  structure  projecting  above  the  wing, 
to  which  the  top  load  wires  are  attached. 

WING  RIB:  A  fore-and-aft  member  of  the  wing  structure 
used  to  support  the  covering  and  to  give  the  wing  section 
its  form. 

WING  SPAR  OR  WING  BEAM:  A  transverse  member  of  the 
wing  structure. 

YAW  :     To  swing  off  the  course  about  the  vertical  axis. 

Angle  of. — The  temporary  angular  deviation  of  the  fore- 
and-aft  axis  from  the  course. 


APPENDIX  II 

THRUST  CHARACTERISTICS 


91 


THRUST    CHARACTERISTICS 


93 


c/,700 

Q 


600 


C/3  500 


400 


200 


100 


40  60  80  100 

VELOCITY     -    MILES  PER  HOUR 


Fig.  34.  Total  resistance  or  thrust  is  the  sum  of  wing-resistance 
and  parasite  resistance.  The  curves  represent  case  when 
W  =  2000  Ibs.;  W/S  =  6;  parasite  resistance  =  0.04  F2. 


THRUST    CHARACTERISTICS 


95 


500 


300 


g 


100 


^0  40  $0  8p  100 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  35-  Variation  of  thrust  with  velocity.  The  three 
curves  show  effect  of  changing  weight  (W  =  1000,  2000 
and  3000  Ibs.)  when  loading  is  kept  constant(  W/S  —  6) ; 
parasite  resistance  =  0.04  F2. 


THRUST    CHARACTERISTICS 


97 


SCO 


•400 


o 


500 


CO 


4* 


.       _ 
VELOCITY  -  -  MILES  PER  HOUR 


Fig.  36.  Variation  of  thrust  with  velocity.  The  three  curves 
show  effect  of  changing  loading  (W/S  =  4,  6  and  8)  when 
weight  is  kept  constant  (W  =  2000  Ibs.);  parasite  resist- 
ance =  0.04  F2. 


THRUST    CHARACTERISTICS 


99 


I 

i 


600 


500 


400 


360 


8 


200 


100 


4          20         40        40          SO        100 

VELOCITY  -  -  MILES  PER  HOUR 


ig-  37-  Variation  of  thrust  with  velocity.  The  three 
curves  show  effect  of  changing  weight  (W  =  1333, 
2000  and  2666  Ibs.)  and  loading  in  proportion  (W/S 
=  4,  6  and  8),  wing-area  being  constant;  parasite 
resistance  =  0.04  F2. 


THRUST    CHARACTERISTICS 


101 


£00 


600 


400 


CO 

D 


300 


100 


20        40        60       .60        100 

VELOCITY  -    ~  MILES  PER  HOUR 


Fig.  38.  Variation  of  thrust  with  velocity.  The  three 
curves  show  effect  of  changing  parasite  resistance 
(R  =  0.02  F2,  R  =  0.04  F2  and  R  =  0.06  F2);  weight 
and  loading  constant  (W  =  2000  Ibs.;  W/S  =  6). 


,         c    (>«.-  f    ^i  ,-  *»  ^     » 


APPENDIX  III 
POWER  CHARACTERISTICS 


Horse  power  required  is  equal  to  thrust,  in  pounds, 
multiplied  by  velocity,  in  miles  per  hour,  divided  by  375. 
The  following  U-shaped  curves  show  the  variation  of  re- 
quired power  with  velocity.  (The  power  available  forms  a 
U-shaped  curve,  as  shown  on  outside  cover.) 


103 


POWER  CHARACTERISTICS 


105 


160  r 


itc 


100 


60 


o 

W      60 


MINIMUM  VELOCITY  -#• 


VELOCITY  - 


«io  ea          iqo 

-  MILES  PER  HOUR 


Fig.  39.     Required  power  at  different  velocities,   when 
W  =  2000  Ibs.;  W/S  =  6;  parasite  resistance  =  0.04  V2. 


POWER  CHARACTERISTICS 


107 


100 


ec 


tO  40  6C  80  100 

VELOCITY  -  -  MILES  PER   HOUR 


Fig.  40.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  weight 
(W  =  1000,  2000  and  3000  Ibs.)  when  loading  is  kept 
constant  (W/S  =  6);  parasite  resistance  =  0.04  F2. 


POWER  CHARACTERISTICS 


109 


ICO 


8 
ES 

2 


I. 


20  40  60  80  109 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  41.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  loading 
(W/S  =  4,  6  and  8)  when  weight  is  kept  constant 
(W  =  2OOolbs.);  parasite  resistance  =  0.04  F2. 


POWER  CHARACTERISTICS 


111 


140 


120 


100 


M 

I 


I. 


20 


20  40  60  80  100 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  42.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  weight 
(W  =  1333,  2000  and  2666  Ibs.)  and  loading  in  propor- 
tion (W/S  =  4,  6  and  8),  wing-area  being  constant; 
parasite  resistance  =  0.04  V2. 


POWER  CHARACTERISTICS 


113 


90 


Or 


« 

I 

1 


40 


10 


80 


VELOCITY  -  -  MILES  PER  HOUR 


Fig.  43.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  parasite  re- 
sistance (R  =  0.02  F2,  R  =  0.04F2  and  R  =  0.06  F2); 
weight  and  loading  constant  (W  =  2000  Ibs.;  W/S  =  6). 


APPENDIX  IV. 
CONTROL  AND  OTHER  DIAGRAMS. 


115 


CONTROL 


117 


Fig.  44.  Distribution  of  pressure 
on  a  single  wing.  Negative  pres- 
sure on  the  upper  surface  pro- 
duces more  lift  than  the  positive 
pressure  on  the  lower  surface. 


PRESSURE 


PRESSURE: 


Fig.  45.  Distribution  of  pressure  on  a 
biplane.  Negative  pressure  on  upper 
surface  of  lower  wing  is  much  reduced 
by  interference  with  the  uppper  wing. 


CONTROL 


119 


1 


Fig.  46.     Biplane  Construction. 


CONTROL 


121 


a 


Fig.  47.     Balanced  Control. 


BALANCED  RUDDER 


FOOT  BAR 


RODDER  POST 


Fig.  48.    Operation  of  rudder. 


CONTROL 


123 


EUCVATcm  RAISED 

NORXAL  POSITION 
CLEVATOR  LOV2F.ED 


Fig.  49.  Stick  control  for  operating  elevator.  To  nose 
down,  push  stick  forward  thus  lowering  elevator.  To 
nose  up,  pull  stick  back  thus  raising  elevator. 


FLAP  AILERON 


WHSEL  CONTROL 


STICK  CONTROL 


Fig.  50.  Operation  of  ailerons  for  lateral  control.  Turning 
wheel  or  moving  stick  to  one  side  causes  wing  to  descend  on 
that  side. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


: 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


